I've been meaning to post this article for a while. Most animals are able to produce pigments for specific colors, or they attain the colors from something that they eat. The pink of flamingo feathers and bodies comes from the birds' diets; pigments in shrimp color their feathers the vivid shade. Blue is a bit of an anomaly. To read more, check out How Animals Hacked the Rainbow and Got Stumped on Blue on NPR.
Evan Leeson/Bob Peterson/lowjumpingfrog/Look Into My Eyes/Flickr