If you flit around or flit between one place and another, you go to lots of places without staying for very long in any of them.

If someone flits from one thing or situation to another, they move or turn their attention from one to the other very quickly.

If something such as a bird or a bat flits about, it flies quickly from one place to another.

If an expression flits across your face or an idea flits through your mind, it is there for a short time and then goes again.