Hey Kingdra, you are going down son! :P
Ok, firstly, Dragon type Pokemon aren't going to help you much.
Unless you are faster than Claire's Pokemon. I suggest planning out for an Ice type Pokemon. If you still want a Dragon type, read on. I have also included some possible Ice types to take into account.
- Extreme Speed Dragonite (obtainable).
Obtained later in the game:
These are the only Dragon types you can obtain in HGSS via trading or catching ingame. Not many choices right? Well, overall, my best bet for Pokemon you can catch ingame would be Kingdra itself. If you can, try and EV train it a bit in Speed while training the Horsea and Seadra up. If you manage to outspeed Claire's Kingdra, then your in luck and you will find yourself with a OHKO Dragon Pulse. Not only that, but the Extreme Speed Dragonite you obtain is great to use against Claire, at least taking two Dragon type STAB hits.
Via trading, Garchomp go. Garchomp will wreck the Gym fully. It will outspeed almost every Pokemon and with STAB Dragon Claw, you can sweep through.
Also, one more thing to add, any Pokemon that can learn Outrage via Level up or Move Tutor will come in extremely handy. Just start an Outrage sweep and the gym shouldn't be too hard. This is what I recommend.
Now I'm guessing this is enough. You have so many choices of Ice types to choose from. Use any of these, train them and the gym will be a piece of cake. I strongly recommend Mamoswine. This is what I used in my play through and by experience I can strongly recommend this to you. Other great options would be Weavile, fast and strong and Dewgong. Being able to resist Water type attacks and pull of STAB Ice Beam to OHKO almost the whole team. Now Ice won't come useful against Kingdra, but will help you save other team members to defeat it later on.
Whoa this took me a while to type.
Ice type Pokemon.
Dragon type Pokemon.