Flamingos are born with gray feathers. They turn pink in the wild because of their diet. They eat brine shrimp and algae that contain a class of compounds called carotenoids, such as the beta-carotene that gives carrots and other orange vegetabes their color. The brine shrimp eat algae that contain carotenoids. An enzyme in Flamingos' livers breaks the carotenoids down into pink-orange molecules that are deposited in their feathers, legs and bills.
Flamigos kept in captivity, for example in zoos, are fed beta-carotene or other carotenoids to produce the pink color. Without this their feathers would eventually turn back to gray.
People eat food with beta carotene, which is converted to vitamin A. It's possible for someone who consumes a lot of beta-carotene to develop an orange-looking skin coloration.