Yes it can.
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No, Beautifly cannot learn Fly.
no
Yes.
Empoleon is not able to learn the HM move Fly. Typically only Flying type Pokemon can learn the move Fly with only a small handful being the exception. And most of those exceptions have the ability Levitate.
No but it's next evolvled form will be able to learn fly ok ignore that is is sooo wrong vibrava can learn fly with a TM however trapinch can't and vibrava can not learn dig but trapinch can it is very confusing... the evovtion of vibrava can also learn fly (by the way i am a girl they know alot about Pokemon 2) XD