No, Flash Fire and Thick Fat don't have any effect. Apart from the abilities mentioned in the first post, nothing else has a special effect.
I find it somewhat odd that Dry Skin wouldn't absorb Water type Stealth Rock, personally. It's a heal-and-absorb effect identical to Water Absorb. I get why, for instance, Sap Sipper doesn't get an Attack boost and clear, even though that would be kind of cool, but I'd expect Dry Skin to be in line with Water Absorb's behavior.
Also, could my prior post be linked to in the OP or the information copy-pasted into the OP, for the convenience of new players?
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Nidoking and Nidoqueen were never called upon much in OU for setting Stealth Rock anyway, but even though they are now unique setters of a type of Stealth Rock, I imagine they'll see even less use for that than in Standard. Poison is just bad, with anti-Fairy coverage much better handled by the numerous Steel choices and the anti-Grass coverage better handled by the Fire, Ice, and Bug options. Too bad.
I alluded to this in the prior post, but I suspect it's going to have a notable impact on the metagame that Smeargle and Chansey get Normal type Stealth Rock: specifically, they won't do it. This slightly hurts Chansey's utility, since normally Stealth Rock carrying variants can use an enemy Special attacker to switch in and get work in by setting Stealth Rock, and here that's just a terrible idea, but Smeargle particularly suffers, as its hazard stacking sets have a much lower payoff. The other Normal types are not exactly popular Stealth Rock setters anyway, and they'll be even less appealing now, Kecleon aside. Miltank is the main other one that suffers, as it's a decent stallmon.
I suspect Garchomp overall suffers from setting Dragon Stealth Rock. It has to deal with one resistance and one immunity instead of three resistances, but it also has only one super effective instead of four, and there's only four Pokemon in Standard that doubly resist Stealth Rock (Steelix, Lucario, Cobalion, Excadrill) where every random Fairy (Gardevoir, Clefable, Klefki...) is immune to Dragon Stealth Rock. In practice I suspect its performance goes down, even though it does better against most Ground and Fighting types. Druddigon suffers as well, of course, but it's not a popular Stealth Rock setter.
Psychic Stealth Rock is kind of interesting. Azelf could be a neat suicide lead for teams that are otherwise overly weak to Fighting types -a Sandstorm-y team, say- while Mew and Celebi are... well. Overall I suspect it's a downgrade compared to regular Stealth Rock, but they might still be a better fit to some teams than a Pokemon that sets Rock type Stealth Rock. Uxie and Mesprit are barely worth commentary.
Ferrothorn getting Grass type Stealth Rock is, on the face of it, a bit of a bummer, but is actually pretty neat. For one thing, it's an obnoxious combination with its Thunder Wave access -if you're safe to switch in on Thunder Wave you're probably weak to Ferrothorn's Stealth Rock- and for another being able to pressure bulky Water types, not to mention punish one of the few Rapid Spinners that's viable (Starmie), is actually really cool. Since there's no Electric Stealth Rock, its utility against Water types is unique, too. By far its most noteworthy characteristic is the utility for supporting a Physical set-up sweeper: if they can do at least 50~% to Quagsire, it can't actually switch in on them so long as Grass Stealth Rock is up, which is incredible. Torterra, on the other hand, resents missing a chance to shine because of Ferrothorn. So close to relevance, Torterra, but not quite.
Mamoswine's Ice type Stealth Rock strikes me as likely to be one of the most relevant in the tier. Ice is an excellent offensive type, with arguably a more useful spread of super effectives/ineffectives than Rock type (Ice resisting Ice is pretty ignorable, since Ice types aren't very good for the most part, for example) and in particular retains pressure on Flying types (They of the Defog) while adding in pressure on Dragon types. Since a number of really good Dragon types are doubly weak to Ice, and indeed a surprising number of OU/UU Pokemon are doubly weak to Ice, this is quite reliable/powerful. The fact that it's ineffective against Water and Fire is a bit of a flaw, though, particularly since Water types include a lot of bulky Pokemon while Fire types are liable to shoot up a bit in viability now that Stealth Rock isn't
automatically ripping half the health off of Volcarona, Charizard, etc.
It's difficult to estimate the relevancy of Bisharp's Dark type Stealth Rock. For one thing, Bisharp isn't exactly the most ideal hazard setter. For another, pressuring Ghost and Psychic types is a bit narrow. Pressuring Ghost type is legitimately nice, particularly since Gengar is immune to Spikes so if you're a hazard stacking team you might consider Bisharp just for that sort of reason, but pressuring Psychics is... neat, but Magic Guard is found on, for instance, Alakazam. Pressuring Slowbro is definitely a perk, though. The fact that it's one of the only Stealth Rock types Steel doesn't resist is a perk as well.
Clefable's Fairy type Stealth Rock has to struggle with Clefable getting into 4MSS territory for trying to take advantage, but the ability to pressure Dragons, Fighting types, and Dark types is pretty cool. In particular, Clefable is potentially a bit of a nightmare for Mega Sableye, which can't necessarily afford to switch in on it for fear of Moon Blast, but it can't necessarily afford to
not switch in on it for fear of being pressured by Fairy type Stealth Rock. Being resisted by Poison types is reasonably minor, since not many are strongly viable in OU anyway, though being resisted by Fire types is a bit of a problem. Being resisted by Steel types... well, most Stealth Rock types are. So that works out pretty well.
Heatran and Infernape are liable to be the kings of Fire type Stealth Rock, and Fire type Stealth Rock is liable to be markedly influential. In some ways it overlaps painfully with Ice type, with Ice type overall coming out ahead, but Fire type Stealth Rock has one key advantage: it's the only type effective against Steel types that nothing can be immune to. Note, for instance, that Skarmory is only vulnerable to Fire Stealth Rock out of all readily accessible Stealth Rock types, barring Gravity, Iron Ball, etc. Scizor is doubly weak to Fire with no other weaknesses at all, as well, and pressuring it so harshly is obvious fantastic. Being resisted by Dragon, Fire, Water, and Rock is all a bit of a pain, and teams leaning on Fire Stealth Rock should take care to have other answers to those, but the utility for pressuring Steel types alone is enormous.
Water type Stealth Rock has no one clear "winner", as far as a user that is obviously excellent as a suicide lead or a stallmon. Empoleon is the only one that lacks a double weakness, and the closest to being a wall out of the bunch. Being neutral against Steel types, like with Dark type, is obviously valuable, and the ability to pressure Rock and Ground types sets it apart from Rock Stealth Rock -Rock is overall better at pressuring Fire types- but being resisted by Grass and Water is a bit of a nuisance. It's too bad not many Pokemon doubly weak to Water are particularly popular -Pokemon like Golem are rarely run anyway. Between that point and the flaws with the potential setters, I suspect Water Stealth Rock won't be very influential.
Bug type Stealth Rock, as I already said, is probably more of a downgrade to Shuckle and Forretress than anything else. Bug is super effective against three types and resisted by
seven. The utility against Dark is probably better handled by Clefable, the utility against Grass is probably better handled by Heatran and Infernape, and the utility against Psychic is flawed by Magic Guard and anyway Bisharp's Dark type Stealth Rock is probably better anyway. Unless you're concerned about some unholy trinity of all
three of those types on an enemy team, it's going to be very hard to argue for Bug type Stealth Rock, which is unfortunate given how useful Shuckle and Forretress are as hazard stackers in OU.
Steel type Stealth Rock is diverse in its options, and is liable to be relevant just because the king of hazard management sets it now. Overall Steel is a bit sub-optimal as a Stealth Rock type, but the ability to pressure Fairies -Clefable, say- is not to be underestimated, given nothing else is even halfway decent
and effective against Fairies. If you want to pressure Ice or Rock, though, there's better types for that.
Ground type Stealth Rock is, again, diverse in its options, and has two of the other classic Stealth Rock setting, recovery-capable walls: Hippowdon and Gliscor. To its detriment, it has to deal with Flying types and Levitators being immune to it, but it's the
only type effective against Electric, as well as pressuring Rock, Steel, Poison, and Fire types. Ultimately probably it's biggest flaw is how many of the broadly viable instances of those types are immune to Ground anyway -you'd rather have good ol' Rock type Stealth Rock for Thundurus, Zapdos, Charizard, Crobat, Skarmory... Still. it also incidentally provides incentive for setting Gravity. (As Showdown is down right now, I can't go dexsearching for Gravity-setting force-switchers, alas) With Gravity up, Ground type Stealth Rock becomes
the best Stealth Rock type, bar none, with only Bug and Grass types having any protection from it at all. This is not to be underestimated.
Rock type Stealth Rock is of course the classic kind. It's worth commentary that Cradily is the only Pokemon that can set it that is both reasonably bulky and has reliable recovery, though, making it noticeably harder to keep Rock type Stealth Rock up throughout a match. Getting it up at all is pretty easy, but keeping it up is liable to be a lot harder.
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In turn, here's some implications.
-Those Pokemon severely held back by Stealth Rock in Standard are more viable. (Charizard, Volcarona, etc)
-Some prominent Stealth Rock resists can't count on that anymore. Hippowdon, Keldeo, Ferrothorn... a number of these Pokemon are easier to pressure than in Standard.
-Weirdly enough, Rock type Stealth Rock may end up being one of the least viable/common just because its only Pokemon capable of coming in again and again isn't a high-viability Pokemon, where Steel has Skarmory, Grass has Ferrothorn, Fairy has Clefable, etc. Odd thought.
-Again, Gravity might become a thing, as Mew can set it, Roar targets out, and has bulk and reliable recovery.
I'd also meant to explicitly comment, but ran out of time, that I've excluded various Ubers like Dialga that are unlikely to ever see the light of day in STSR. (I also somehow forgot to include Skarmory first time around, and have corrected this)