In addition to an upper and lower eyelid, birds have a third eyelid called a nictitating membrane. It is translucent and is drawn across the eyes from the lower nasal position upward and rearward to moisten and clean the cornea. This action happens very quickly, sometimes to be almost inperceptible.
Regarding eyelids - for the most part, birds that are active during the day will more often draw the lower eyelid up to blink with less action of the upper eyelid, whereas birds active more during the night (owls and nightjars) drawn the upper eyelid down with less action of the lower eyelid [more of a human blink].
In addition, birds have modified feathers (some are hairlike, others are featherlike, depending on the species) that serve as eyelashes do in humans and some mammals.
In some cases, birds can fly with their eyes closed - studies specifically on Barn Owls (Tyto alba) have shown that the birds close their eyes at the last second before striking their prey, relying on hearing for pinpont accuracy and likely also to protect their eyes from their victim.
Birds like the Peregrine Falcon (Falco perigrinus) can close their nares (nasal openings) during a high-speed stoop (so as not to get too much air into the lungs at 200 mph). I would not be surprised to learn they shut or squint their eyes during flights of that speed.
Hope this was informative.