A pretty good team overall.
Azelf: Perhaps removing Fire Blast and giving it Rain Dance would be useful. I don't know how much attacking you want it to do but U-Turn instead of Psychic is also nice, a sort of Set-Up and Go mindset.
Seaking: They are pretty mean in the Rain, but due to its lack of move range, its not very favorable. Though it may not be Kabutops, it is a very useful Pokemon none the less and I am sure with a Choice Band it will deal deadly damage even when resisted.
Bronzong: Another good Pokemon for setting up. Perhaps giving him Rain Dance instead of Earthquake would also be nice. If he is going to be worrying about Dual Screens, then just being supportive in general would be useful. Can't always take the time to set up with your attackers, right?
Kingdra: And this is what I meant. A very good Pokemon, if not great when it comes to Rain Dance. I am not sure if you should have both Rain Dance and Dragon Dance though. If you teach Bronzong or Azelf Rain Dance then Kindgra could just be a Dragon Dancer just in case. But if you want to keep Rain Dance[, then I'd suggest Surf as a good option against Physical Walls.
Heatran: A Fire Pokemon in the Rain. Though it sounds weird at first, it could still manage to deal some good damage. I wouldn't expect much from Fire Blast or foreseeing other Fire type attacks on a Water based team, but for lack of a better option, I leave this to you.
Ludicolo: One of my favorite Pokemon ever. A good move set, and if you don't need Rain Dance on it, I'd suggest a Hidden Power that'd be useful versus common threats or perhaps a supportive move like Leech Seed or Toxic against walls.
I like the concept of the team overall and I wish it the best of luck and that my advice proves useful.
