Seadra's movepool is horrible... it really doesn't get anything. Most Water-types have moves or a second type that distinguishes them from others. For instance, Starmie can use Thunder Wave and Thunderbolt, Lapras has Thunderbolt and Confuse Ray, Slowbro has Thunder Wave and Amnesia, Kabutops can Swords Dance, Cloyster can Explode, and so on. Seadra can... well, SmokeScreen. And Seadra's stats don't come close to making up for the lack of a better movepool, as they are quite mediocre.
With Hydro Pump, Seadra stands a chance against Tauros, which it can manage to 2HKO on average. Anyone who doesn't feel too good with gambling on Hydro Pump can use Surf. Blizzard is to hit some Pokemon that resist Water for super effective damage and to try to freeze Pokemon if anything.
Using Mimic can help against Starmie switch-ins against Seadra, providing a chance of getting either Thunderbolt or Thunder Wave, both of which can help against it.
Finally, there's SmokeScreen, which is good to annoy anything that could possibly be switched in. It would probably work best if that switched-in Pokémon is an already paralyzed Chansey.
Toxic might just be alright, as Seadra really doesn't get much in terms of movepool, but seeing how Starmie and Chansey are going to be the two Pokémon that are most likely to switch into Seadra, it really isn't such a great idea. You wouldn't want to poison any of them, as Starmie will then be protected from paralysis and Chansey is usually used as a status moves sponge. Still, Seadra's options are limited as already said, so you could consider it.
Seadra also gets Double-Edge and Hyper Beam if you desperately need a physical attack against Chansey, although it really won't do much anyway. Using SmokeScreen against Chansey is more recommended if anything, or else you can attempt to freeze it, assuming it isn't paralyzed.
Finally, Substitute could work decently with SmokeScreen, together with maybe Toxic, in the mix.
Checks and Counters
Water-types with Thunderbolt work well, such as Starmie, Lapras, and Gyarados; just hope that Seadra doesn't Mimic Thunderbolt. Chansey can take everything Seadra dishes out and reply with, as expected, Thunderbolt, and so can Gengar. Alakazam's extraordinary Special makes Hydro Pump just bounce off while it assaults Seadra with Psychic.
In UU, Golduck and Poliwrath work well, since they can set up in front of Seadra with no real consequence (except for SmokeScreen) and then proceed to pummel it. In addition, any Electric-type will also do the trick, of course (just be careful switching Zapdos in a Blizzard due to its Ice weakness).