Continue caring for your flygon as you had for your vibrava. Most flygon have the exact same needs as a vibrava; the only difference is that they’ll require more. That is to say, your flygon should need more space to fly, more sand to nest in, more food (insects and meat primarily, if not kibble) to consume, and more time to train. Just about the only thing your flygon will need less of is perhaps sleep, as it will no longer be saving energy for a future evolution.
Well, that and toys, as final-stage pokémon rarely want toys for enrichment. They mostly prefer battling, truth be told.
The Pokédex According to Bill 