I think it would be a little different because in canon!Rekindle Sam isn't going to make Dragonite carry him so soon after losing a battle, but we can arrange something! (He's probably having trouble getting Dragonite fed. It's no Snorlax but I imagine it still eats a lot because of its size.)

But exchanging family memories sounds really cute :) (Does Ash count as Red's anime counterpart? :|a)