What's the best flying type and fire type for Gen 2? Also best HM slave?

Playing gold/silver/crystal. Need a team that I can take to Stadium 2 right after and beat the gym castle thing

Dodrio smacks ass in Stadium 2, and it flying is funny

https://www.smogon.com/dex/gs/types/flying/
https://www.smogon.com/dex/gs/types/fire/

Skarmory and Typhlosion/Houndoom are your best bets for those types that aren't legendary and don't require a gen 1 game.

As for HM mules, I'd use an Oddish or Bellsprout for Cut and Flash early on, then a Gyarados for Strength and the Water-type HM's (or Rock Smash too if you can fit Surf on one of your main party members). If you can't fit Fly onto one of your main party members, then a Farfetch'd can cover both Cut and Fly at the same time too.