Can a Burst Warrior use any Burst Heart?
Fraud managed to use many types of Burst Hearts. Braviary, Reshiram, Bisharp, Golurk, and the list goes on for a while.
So I think it may be like regular pokemon training, where all pokemon are available so long as you can use a Burst Heart. But I haven't read ReBurst yet so I'm not sure if his case can be considered normal.