...or can a fly fly in zero gravity?
By zero gravity I assume you mean space. Disregarding the fact that the bird would need its own little spacesuit, or it would soon be a bloated and then exploded bird, it still could not fly. Neither could a fly. Both creatures use their wings to push air below and behind them, which propels them forward (this is in effect Newton's Second Law in operation.) Because these creatures are out in space, which is virtually a vacuum, there's nothing for their wings to push against, so no matter how their wings move, they will not.
Astronauts move only by pulling in their tether or pulling themselves along the handholds of the spacecraft.
Gravity attracts an object to another object of greater mass. In case of gravitational force of earth, this amounts to the object falling to earth when there is no force acing on the object to neutralise the effect gravitational force.
Flying is an activity when a bird or any other object overcomes the gravitational force utilizing the air resistance generated by an object (or a part of it like wings of a bird) moving in the air. Flying involves, in addition to opposing the gravitational force also creating other movements to travel from one place to other. Propulsion force required for this is also generated by utilizing movement against air resistance in the form of flapping of wings by birds or rotating of propeller in an aeroplane. In a jet pane the propulsion force is created by the mechanism of the reaction created by gases escaping from a jet.
When there is no gravity there is no need for any force to counter the action of gravity. However propulsion force is still required foe moving from point A to B. If there is sufficient air in the space between the point A and B it will be possible for a bird to create the propulsion force with flapping of its wings, and in this way fly from point A to B. But in absence of air the propulsion force can only be provided by jet mechanism, or some other mechanism utilising reaction of movement of parts of the flying object.