The main difficulty in nocturnal photography (away from prepared ambushes at least) is focusing, for which the camera requires light. You can at close range get by with red but at any realistic distance this means white light from a torch/spotlight. This will cause the nocturnal bird's pupils to shrink shut.
In any case, when the flash goes off actually there isn't a physically deleterious effect, any more than there is when it's used on you. The bird may wait where it is till any dazzle subsides, but I can vouch for that not taking very long (seconds). Or it may just sit there if it is either in its roost or on a traditionally good hunting perch. In either case you should take your pictures quickly and leave it to get on with life.
Personally I always turn flash down a number of stops to minimise the flaring out of eyes backed by a tapetum lucidum. Nobody wants photos in which the subject appears to be fitted with headlights instead of eyes.
Finally, I was once driving down to Cornwall overnight when lightning struck very close to the line of the road. For an instant the entire countryside was lit up like day and then I was completely dazzled - couldn't see a thing - and did an emergency stop on the A303. Rarely been as scared. However, we were able to continue immediately thereafter. It's my belief that wild creatures think - if they consider it at all - that flash is quiet lightning, which will be familiar to them.
John