Which direction does magnetic fields flow?

Answer 1

I think it is a mistake to refer to magnetic field 'flowing. Magnetic fields just are, they can change, and these disturbances might move in space, but the field itself does not flow.

That being said, and assuming you meant to ask in which direction a magnetic field points the answer is that a magnetic field points towards the south pole of a magnet and away from the north pole. A magnetic field cannot be divergent (i.e. there are no sources) and any field line must be closed.