Arrogant Kung-Fu Guy: Dragonite makes it clear that he only allowed himself to be caught by Iris so that she could be a glorified transport for him, to take him to strong opponents that he could then fight and defeat on his own terms, not listening to her commands.
Casanova Wannabe: Alder is depicted as this when he offers to take Cynthia out for lunch, only to be turned down out of hand.
Fight Off the Kryptonite: Dragonite manages to break out of Beartic's Ice Beam, even though Dragons are profoundly weak against Ice-type attacks.
"The Reason You Suck" Speech: Georgia makes clear to Iris that, even though Dragonite won the match, he was not obeying her, and this could cause an issue in the future.
Scissors Cuts Rock: The fact that Dragonite fights off Beartic's Ice Beam suggests it is heavily overpowered. In the games, unless you are the region's Champion, if a Pokémon is too strong, it will refuse to obey you. This could be the case for Dragonite in relation to Iris, especially finishing off Beartic without using his Flamethrower.