Flamingo (wiki) chicks start out grayish-white, then are fed bright red milk, a sort of crop milk made from either parents’ upper digestive tracts. As the chicks grow, they develop their signature pink feathers, as well as adult bills that can filter mud and silt from their food.
Here's an explanation from Live Science:
Flamingos live by lakes, swamps and wetlands, and so they eat mostly algae, insect larvae and small crustaceans, such as shrimp and mollusks.
The red and blue-green algae they consume is loaded with beta carotene, an organic chemical that contains a reddish-orange pigment. (Beta carotene is also present in many plants, but especially in tomatoes, spinach, pumpkins, sweet potato and, of course, carrots.) The mollusks and crustaceans flamingos snack on contain similar pigment-packing carotenoids.
The bird’s digestive system extracts pigment from carotenoid-containing food and it eventually dissolves in fats. The fats are then deposited in new feathers as they grow, and the flamingo’s color slowly shifts to pink.
Related: Don Featherstone, creator of the plastic pink flamingo, and his wife wore matching outfits every day for 37 years.
h/t The Kid Should See This.