I occasionally use flash in low-light conditions, or when spotlighting. I can only comment based on the reactions I’ve seen in the organisms I photograph, so I’d be interested in hearing actual science behind it.
The argument I’ve heard from several “spotlighters” (tour guides doing owl or noct. mammal tours) is that a short burst of light is not nearly as harmful than a continuous exposure (e.g. a torch/flashlight pointed at the critter). The general consensus I’ve learned is using red light to find something, then (white) flash for photography.
This seems to be fair because you can tell when something is afraid of and directly changes its behaviour from light. For owls, they seem to turn away and fly off if you keep a (white) torch on them, while using red light and several camera flashes doesn’t affect their behaviour. For nocturnal mammals I have noticed a similar case although I have less experience there.
I always thought a sudden burst of light would be worse since it is sudden, with no period for the eyes to adapt. But based on the behaviour I see, sudden bursts of light rarely seem to cause a negative effect unless this is abused. If something is running away from you, you’ve already made enough mistakes, let alone with light. Diurnal birds often flinch at the first burst of light, but after the second or third they no longer react to it.