The most favorable matchups for kingdra are fire (if you get a water moveset) or water (kind of), if you get dragon moveset. For dragonite, you are better off using an Ice pokemon, if you don't have a good ice pokemon and you are good at dodging, you could use kingdra, still it's a sub par choice in my opinion.
Kingdra Question
So I made my first Kingdra, 1945CP, 84IV DB/O moveset and I was wondering what it is good for.
Does it do well vs dragonite? What other matchups are favourable?
Answers
It's not ideal vs dragonite since dragonite is going to hit back with dragon moves that it's weak to. Dragonite in any case is absolutely annhilated by anything with good ice moves. Piloswine, cloyster, dewgong, even garbage like high-level sneasels and jynxes - all of these are kryptonite to dragonites.
Kingdra is IMO most interesting because of the double resist to fire and water; I don't have one to try out, but I suspect his best matchups are against water (with DB/O) and fire (with HP) pokemon whose attacks just bounce off of him, and to cause consternation among attackers who aren't really sure, on the spot, what to use against a kingdra (I'll bet grass would be a common pick of such attackers, who don't realize the dragon dual typing means he's not weak to grass).