Item clause is silly, you need your damp rocks and life orbs on a successful rain team =/. Iirc, most people on wifi don't play by item clause anyway, they just have that 'no more than 2 focus sash' rule, so you should be fine. If not, try and get matches with people who don't play by the clause. There's no point in disadvantaging yourself and ruining a perfectly good strategy for an arbitrary non-standard clause.
I know this is for wifi, so you can't help having an Impish Jirachi, but I would recommend you replace Thunder with Stealth Rock. Bronzong is possibly the best user of Rain Dance in OU, and yet you have him using rocks instead or rain. A rain team wants its rocks right at the start of the match, and having a bulky replenisher like Bronzong will be really helpful for your team. So here, go for Stealth Rock > Thunder on jirachi, and Rain Dance > Stealth Rock on Bronzong. A non-STAB Thunder off a -SpA natured Jirachi with little investment won't be hurting much anyway; best let Jirachi do all your supporting needs at the start of the battle and then have it simply U-turn out.
If you are using Ice Beam on Kingdra for Grass-types, there's little point in keeping it over Signal Beam. Celebi is really the only OU Grass type that requires a special move to deal with it, and so hitting it 4x effective with Signal Beam will help you out a lot, since right now, Ice Beam only does 52-63%, which is low enough for Celebi to Recover stall you out of rain and wear you down with your own Life Orb. I would also strongly consider replacing Surf with Hydro Pump. The added power of Hydro Pump is really helpful in getting some key KOs in the rain, since you are not running a +SpA nature. For example, in the rain, Hydro Pump will always OHKO max HP Zapdos with SR whereas Surf would never, Hydro Pump has a 75% chance to OHKO max HP Metagross with SR whereas Surf has none, and Hydro Pump will always OHKO max HP Scizor whereas Surf falls just short. It's on Pokemon like these, who have much higher physical defense or invest in it much more, that you wouldn't use Waterfall (your main sweeping move in the rain), and so Hydro Pump's additional power is really welcome in getting these crucial KOs.
Don't waste time using Earthquake with Bronzong. You really want Explosion in there, so that Bronzong can set up the support needed then quickly get out of the way and get a sweeper in for free, hopefully blowing a hole in an opposing wall while its at it. Rain teams play far too fast for Earthquake to be of any use - it's not like Heatran is threatening you anytime soon anyway. You've been considering it, and I'd definitely recommend it. Explosion is a great move to have on a rain team.
While Scizor is a cool Pokemon to have set up Rain Dance, I think you would be better off dropping it for another type. Having three Steel-type replenishers might not be the best idea - it means that if the opponent gets Infernape in while you have no rain, you won't be given a chance to get your rain replenished, and you will therefore most likely lose. Jirachi and Bronzong are better users of rain dance because of their bulk, and serve this team better, so Scizor is the one that should go. Starmie has been suggested already I think, and I'd have to agree here. Starmie would fit into this team very well over Scizor:
Starmie @ Damp Rock; Timid; 252 HP / 40 SpA / 216 Spe
Rain Dance / Surf / Thunder / Recover
With Recover it has a fair bit of survivability too, and in the rain it can really make use of double STAB Surf and fully accurate Thunder. With the HP EVs and Recover, it can stick around a while, and set up rain more than once if you need it to.
Obviously, replacing Scizor makes you a bit weaker to Latias. Azumarill isn't doing much for the team here. It is slow even in the rain, and Substitute is clumsy and wastes turns. Drop Azumarill here for a Qwilfish:
Qwilfish @ Life Orb; Adamant; 92 HP / 252 Atk / 164 Spe
Swords Dance / Poison Jab / Waterfall / Explosion
Currently, if your opponent is running a Tentacruel, you will find it quite hard to win. Tentacruel can come in on both Ludicolo and Kingdra and start setting up deadly Toxic Spikes. T Spikes are probably the surefire way of beating a rain team if they go up early enough - the rain sweepers won't be around long enough to do threatening damage when they are losing health to both poison and LO. Qwilfish helps you out greatly simply because of its Poison typing, which will soak the spikes up for you on entry. With the screens up, Qwilfish shouldn't find it too hard to get a Swords Dance in, as long as you don't try to SD up on something that can hit you super effectively. Once it's danced up, very little stands in its way. Standard 148/0 Latias is OHKOed by Poison Jab, as is Celebi, and really everything else dies to double STAB Waterfall. Count your turns of rain, and just as it's about to run out, you can go Boom with Qwilfish and be free to bring in your fast Starmie to replenish rain once again. Azumarill simply does not have the immediate power that Qwilfish brings to the team, and can't deal with Latias. Qwilfish will fit in here great.
That's all I have to recommend for now. I hope some of my suggestions help, good luck with your team =).
