This is the definition for the move Burn Up:
To inflict massive damage, the user burns itself out. After using this move, the user will no longer be Fire type.
I'm wondering what type the user will be after using this move.
If it's a dual type Pokemon like Moltres, then it will lose the Fire type and just become the other type, so Moltres would become a pure Flying type. If it is a pure Fire type, it will become typeless.