Always remember that animals, even your beloved pets, are unpredictable and may behave aggressively if they feel threatened. Never approach a strange animal, particularly if you have your own in hand or on a leash. And don't place yourself between two angry animals. Use leashes to separate them, not your delicate limbs. That glazed look in Fluffy's eyes, followed immediately by a scowl, or worse, a rapid sprint under the bed, is a pretty typical reaction to your camera flash.
Some animals are more sensitive than others to camera flash.
A camera flash is not bright enough to hurt your pet's eyes, unless your pet is a nocturnal creature. No, don't call the tabloids, Fido is not possessed because his eyes look red or green in pictures. He's got redeye or greeneye. The light from your flash bounced off the back of his eyes and at the camera. Next time, try to catch Fido when he's not looking right at the camera.