With flash photography, the photograph is exposed during the short 'pulse' of bright light. This pulse is of extremely short duration, and is over more quickly than the reaction speed of the human body.
So, even if your boyfriend blinks in reaction to the flash, the photograph has long been exposed (ie. 'taken') by the time his eyelids can actually react - so this is not the cause of him having his eyes shut in photographs.
'Redeye' is caused by light bouncing off the retina at the back of the eye - (in the same way as you can see cats' eyes 'glow' at night when they look toward you and a light source.)
In relatively low light conditions - your pupils are 'dilated' or open wide, but will contract when the light intensity increases. Again, however, they cannot rect quickly enough to the flash, so that when the flash fires, some of the light is reflected straight off the retina, causing the redeye effect.
A 'redeye reduction' setting on a camera fires off a series of smaller pulses of light. These allow time for the pupils to contract (get smaller) in reaction to the light, before the main flash fires and the photograph is taken. Thus, less light is reflected from the retina because of the contracted pupils.