The lift force you would need to produce would have to be equal (stable flight) or greater (take off) than the force pulling you back towards the moon. If your mass is average for a male at 62kg, the force from the lunar gravity would be F=ma, = 62kg x 1.622m/s2 = 100N (almost exactly).
lift force = 0.5 x density x lift coefficient x area x velocity^2
This is as far as you can really calculate without specifying shape/size of the wings etc. However this site shows that the human arm can exert around 50N -60N (that's per arm). So with the correct design it seems like you have 1.1 times the required force available. This all ignores the mass of the wings themselves, the percentage of force that is applied in the appropriate direction etc, it at least implies you would be able to hover on the spot until you get tired. I suppose doing so would become comparable to the world record for treading water - after 85 hours you'd be pretty bored.