Hmm... what about Charizard/Dragonite/Gyarados?


I have a knack for curing sleeping problems
All three Pokemon can learn Sleep Talk and Snore, which keeps sleeping from being a problem.

Despite having sleeping problems of my own
Which only leads to confusion.
Charizard and Dragonite can learn Outrage, while Gyarados picks up Thrash. Both moves keep the Pokemon from sleeping during the attack but result in the user's confusion.

Don't ruffle my feathers
All three Pokemon are Flying types.

You'll only succeed in losing the edge
All three Pokemon can learn Double-Edge.

Unless I swagger away.
All three Pokemon can learn Swagger (surprise, surprise).