This pictures show the nictating membranes protecting the eyes from element - wind or dust
Maybe this bird blink due to flash.
The most common evidence of flash on bird eyes are red-eye and silver-eyes effect. This is common as we photograph people in dark environment with flash. The wide pupil reflected the the light from retina, showing the gosty-red eye effect. With pre-flash and post precessing, all that effect can be cancel out.
In bird photography we normally use flash bracket to move the flash from the centre of lenses, thus minimize the effect. With Better Beamer (flash extender) that many photographer use, we can reduce the flash output to minus (-1, -2 etc). This further reduce the effect of flash on bird.
The aim of flash is just to have a minimal fill-in effect, the little the better. Sometime in the dark canopy on rain forest we have no other choice, but to have full flash as a sole source of lighting.
The right and (closed-up below) was photographed with fill in flash.
The left and (closed-up above) - no flash.