Making a character fly and being able to control it whilst doing so

i just wanted to know if it was possible to make a character fly, not hover, and to be able to control the character while it’s flying
and to be able for it to, at the same time, walk/ sprint/ jog
so what i’m basically asking here is:
is it possible to be in control of a character that both walks and flies?, and to have it fly on a whim?