Do you mean controlled flight? After all, a virus or bacterium might be swept along by the faintest movement of air but no one could call that flying.

Our Donegal midges fly very competently on a calm day, but the lightest breeze is usually enough to keep them in their lair. I've written about them before http://www.pete-smith.co.uk/midges.html

Apparently, the Tanzanian parasitic wasp is the smallest winged insect and appears on many websites, but I can't find one that I'd cite as an authority.

Certain parasitoid wasps are the smallest known insects, last time I looked. Try looking up the family Mymaridae. Some web search facilities will show you images of Dicopomorpha  species, some of which may be only about a tenth of a mm in length fully grown. As far as I know all those really tiny species (roughly the size of a Paramecium) grow up in the eggs of insects -- quite small insects. 

The reason to look up their pictures is to get some idea of their wings. They are very different from more familiar wings; so small that the significance of the  laws of aerodynamics is different for them. Their flight differs more from that of a mosquito than the mosquito's flight differs from that of an eagle. As some aerodynamicists put it, they fly as though they were moving through syrup rather than air. Their wings are more like hair-fringed paddles than anything you will see on more familiar fliers.