Man, finding a color for every letter is harder than I thought. Here, have some pink.
While I could not find a myth or folktale about the flamingo and its color, there is a delightful tale that I can include here. While most websites will tell you it is an "Argentinian folktale," it was actually written about a hundred years ago by an author called Horacio Quiroga, from Uruguay. His book, Cuentos de la selva, is a great read. As a storyteller, I have no problem telling tales that migrated from literature into oral tradition. That is the nature of good stories.
According to this one, the animals of the jungle decided to have a dance party. All of them put on their best colors and dresses, except for the flamingos, who are not particularly smart. Looking for something colorful to wear, they decided they were going to accentuate their lovely long legs with some colorful stockings. They went for help to Owl, who just happened to have some prime accessories lying around, and gladly handed them over; but he also warned the flamingos not to stop dancing at the party. The birds put on their brand new yellow-red-black striped stockings, and went to show them off.
The snakes took revenge on the flamingos by biting them repeatedly (as you should, when someone shows up wearing your uncle's skin for a stocking). The flamingos fled to the river and cooled their wounds in the water. In fact, they have been living there ever since, soaking their poison-red legs.
Read the original story here.