The simple rule for using a flash to photograph wildlife is just that- don’t. If it is a mammal, and truly wild (not a zoo or farm animal, or animal that has become overly acclimated to having humans present) the flash will usually spook it, losing you further opportunities for more pictures. It will also unduly stress the animal.
The times when a flash is most useful are at night or in low light. Flashing animals at this time can interfere with their night vision, making their night time activities more difficult. This can threaten their very survival in a world where their life depends on their senses.
Birds are not as likely to spook, but their eyes are often of such a design that their version of red eye is much more extreme than that of people. This is especially true of the more nocturnal species.
Flashes have a limited effective range. Often times, being close enough for the flash to work properly you have to be too close to the animal for the animals comfort.
As I said, this is just the simple guideline. There are exceptions to any rule, just think very carefully before flashing any wild creature.