Even though Sky Attack isn't really too competitive a move, it could've seen some fun use on Braviary. Aside from the fact it usually has enough bulk to survive at least one attack, it can pull off the annoying 2-turn strike of Sky Attack, and because Sky Attack has a flinch chance, it gets boosted by Sheer Force. Should Sheer Force be a 30% boost, then you've got an attack that does 140 x 1.5 x 1.3 = 273 base power, and if it's a 33%, then make that 279.3 Base Power. Should you actually decide to go for the whole two turn charge up idea, then you can add in a life orb for around 350 Base Power, or a choice band for a 409 base power move. You could always go with a power herb for an instant Sky Attack too, but really, you'd want Brave Bird for a move you could actually use in one turn anyway, especially since you'd do more damage over two turns with Brave Bird unless you used a Choice Band Sky Attack (but why would you lock yourself into a move that takes two turns to use? <_<)
It's not a good idea but it could be a fun gimmick, especially since with a choice band you're looking at an attack of 409 base power coming off of an attack stat of either 345 or 379. That's a severe dent to anything. However since Braviary does NOT get Sky Attack, and honestly, who knows why?
Also some people mentioned Braviary not getting Agility. While it's not much better for compensation, there is always the use of Scary Face (which gives the foe -2 instead of Braviary a +2). Since the whole point of an agility set would be to boost on a switch/resist, you could also Scary Face on a switch/resist and outspeed whatever comes out. Cutting a foe's speed in half also really lets you add points to bulkier sets as well. Scary Face also appears to have 100% accuracy now (used to be 90% apparently), so it is guaranteed to work.
First of all some threats at -2 speed...
+Speed Latios: 350 / 2 = 175 Speed
+Speed Jolteon/Aerodactyl = 394/2 = Approx 197 Speed
+Speed Accelgor = 427 / 2 = 213.5 Speed
+Speed Scarfed Heatran = 417 / 2 = 208.5 Speed
+Speed Ninjask = 460 / 2 = 230 Speed
+Speed Scarf Garchomp = ~499 / 2 = ~249 Speed
+Speed Scarf Haxorus = 483 / 2 = 241.5 Speed
+Speed Scarf Hydreigon = 486 / 2 = 243 Speed
Weather Speed Boosters simply lose their boost. If you couldn't outspeed them in the first place you won't outspeed them after Scary Face either
So basically with Scary Face in play and assuming 31 Speed IVs, you are already at 195 Speed with no investment at a neutral nature. That means 12 Speed EVs lets you outpace base 130s after Scary Face (but honestly why would Jolteon switch in on Braviary? Aerodactyl does resist normal/flying however, and can probably OHKO with STAB Stone Edges while I'm not too sure if you can even 2HKO it with Brave Bird, though you could probably OHKO with a Fight Jewel boosted Superpower), and thus to outpace common scarfed threats with speed boosting natures you'll go from any where from...
-56 Speed EVs to outpace +Speed Scarf Heatran (which I hear is uncommon actually this gen, but it can switch into Return/Brave Bird, but fears Superpower).
-188 Speed EVs to outpace +Speed Scarf Haxorus (and well, Haxorus if it used Dragon Dance I guess. Though if you're both out at the same time, I don't think you would typically decide to Scary Face a Haxorus immediately while it DDs up <_<, Haxorus' defenses mean it probably won't switch in though, especially since it doesn't resist anything you have and it will be taking a huge hit HP wise even if it does live).
-196 Speed EVs to outpace +Speed Scarf Hydreigon (who is also usually a revenge killer. It probably won't switch in either due to fear of Superpower anyway, but otherwise Hydreigon is decently bulky and could probably handle at least one hit from Braviary).
-220 Speed EVs to outpace +Speed Scarf Garchomp (who again, is mostly a revenge killer who doesn't want to switch in on most Braviary attacks anyway. Not sure if standard Scarfchomp can actually survive Brave Birds though. Might need a Life Orb or Flight Jewel to do so.
So it seems like the things that Braviary can outspeed after Scary Face are quite a few things, some you have to invest a lot of points into, others, not so much. However most of the things I listed so far either wouldn't normally switch into Braviary or are not as common these days. So what things might actually switch onto Braviary at all that do the following:
-Outspeed Braviary without Scary Face
-Carry a resistance or immunity to Braviary's main attacks
-Can immediately threaten Braviary with a possible KO.
-Gengar can switch into normal type attacks, and a LO thunderbolt will hurt hard (359 Atk vs 185 Def & 404 HP (95 Base Power): 342 - 404 (84.65% - 100.00%)) so basically you die after Stealth Rocks/Sandstorm if Thunderbolt didn't kill you outright.
-Arcanine can switch in thanks to Intimidate and threaten with Wild Charge, however I did some damage calcs and... [319 Atk vs 185 Def & 404 HP (90 Base Power): 290 - 342 (71.78% - 84.65%)] so you can actually survive the Wild Charge. If Dream World Braviary were out, Intimidate wouldn't matter and you would probably OHKO it after outspeeding with Scary Face.
-Raikou can switch in and OHKO with thunderbolt and survive resisted Brave Birds without much investment. However if you Scary Face it on the switch, it won't outspeed and OHKO, however I don't think Braviary actually packs enough punch to OHKO Raikou either. Thrash might do the trick on other sets but as most people have said, locked into a normal type attack = bad bad bad.
-Latios can switch into Superpower, but with a life orb, Brave Bird will probably one shot it after SR. Scary Face does ease prediction in case you think your opponent might now what you're up to.
-Latias has enough bulk to survive things coming in on the switch, but it can't OHKO with Thunderbolt (most Latias don't even run thunderbolt anyway). Hitting it with Scary Face lets you outspeed it, but Braviary doesn't actually have any options to OHKO it without a Flight Jewel boosted Brave Bird or Normal Jewel boosted Return/Thrash (not sure if Return will OHKO with Normal Jewel). Since Latias tends to run more defense spreads, it's unlikely you can OHKO it, rather, you'd need a 2HKO, preferably one hit on the switch because Latias can definitely 2HKO you.
As long as it's switching in though, you have the advantage, since the only way Latias can OHKO Braviary is if it's using a Specs set, in which case, Draco Meteor will probably drop you.
-Lucario resists one of Braviary's STAB options but falls to Superpower. However it can still outspeed Braviary, but I'm not sure if anything unboosted will KO Braviary, as Braviary's 100 Base HP plus it's okay defenses actually let it survive quite a few things (albeit barely), as evidenced by Gengar's maximum damage with it's standard Timid LO Thunderbolt just barely getting to max out at 404 damage to Braviary without anything but HP investment. If you're hindered by Rocks though, Lucario can probably drop you with Ice Punch, Specs Aura Sphere, or just a raw LO Close Combat.
-Thundurus resists Braivary's Flying STAB as well as Superpower and can OHKO with it's powerful STAB thunderbolt. However, hitting it with Return (without a life orb or any other boosts to Braviary's attack) lands you a nice calculation of [379 Atk vs 175 Def & 299 HP (107 Base Power): 249 - 294 (83.28% - 98.33%)], a clean KO after Stealth Rocks. So if you need to ease prediction, you can scary face on the switch then clean KO with Return if you have SR support. Should you have a life orb, then Return is a clean OHKO even without rocks.
-Terrakion is probably Braviary's number one worst enemy to face. It can resist Normal attacks and tank Brave Bird thanks to it's good bulk. It then outspeeds you and wrecks you with Stone Edge (if you don't switch out). However, Scary Face lets you turn the tables but netting you the opportunity to slam it with Superpower. I'm not completely sure, but I believe after LO, and SR, Superpower can OHKO Terrakion, if nothing else, it cripples it quite a bit (as it'll be at -2 speed and low health).
-Cobalion is another big threat to Braviary. Sporting crazy high defenses that even Skarmory is in awe of, Braviary might not even manage 2HKOs. However if they're an offensive Cobalion, your main worry is Stone Edge, which thankfully does not KO without Stealth Rocks (not sure if it KOs WITH Stealth Rocks either if you have full HP investment). Braviary will NOT be able to OHKO Cobalion with Superpower unless it has a Fight Jewel/Choice Band, but if you scary face Cobalion first, you may have a shot at hitting it with two Superpowers in a row (if it's Stone Edge doesn't kill you first, nor does any LO Recoil if you're using a LO).
-Landorus can be outsped if you Scary Face it on the switch (as for why it would switch in on you... I'm not really sure), but calcs need to be done to see if it's possibly OHKO'd by anything Braviary has. Either way, Sand Power Stone Edge will drop you.
Overall from what I can tell, Braviary's inability to boost it's speed without Tailwind or a Scarf is not it's biggest problem (just having low speed is the problem, trying to boost it isn't usually a great idea since you don't usually get free turns TO boost it), so running Scary Face (while a neat concept that DOES help against some notable foes, like Terrakion) is probably not too necessary, but it can net some cool surprise kills and cripples while offering some team support.
Braviary's actually got the ability to 2HKO or OHKO many offensive threats while having enough bulk to endure at least one offensive opponent as well. But like most things with good offense and decent bulk, Braviary is prone to residual damage (especially since it relies on Life Orb for some 2HKOs/OHKOs, otherwise you have to use Type Jewels which are only one shots), Stealth Rocks, and revenge kills. Agility could remedy some revenge kill problems, but alas, it does not get Agility.
Braviary's problems will probably never be anything that stands a direct threat to it. It'll be the usual problems for things trying to brute force their way through things, walls. Braviary's best option against Skarmory is Fight Jewel Superpower or Sheer Force Rock Slide, against Nattorei it fears additional residual damage, even though it has Superpower on it's side. Meanwhile it's not easy getting Braviary in either, thanks to residual damage possibly being shot off from any and all directions, it's worse when you've also got to deal with Will-O-Wispers and Thunderwaves being thrown around.
So it seems like some of the best times to bring in Braviary are to revenge things like Conkeldurr, Breloom, and fragile sweepers (if you're using a choice scarf).