Apparently theyre rather tasty.
Try this.
Oddly, there is a distinct paucity of flamingo recipes. Upon reflection, it seemed logical that one could take a decent recipe for any waterfowl and simply substitute a flamingo for the bird in question. Here is a recipe for roast flamingo, adapted from a cookbook (Le M�nagier de Paris) dating to the late 14th century:
ROAST SWAN FLAMINGO
Take a swan flamingo and prepare it and put it on to roast until it is all cooked, then make a paste of eggs, as clear as paper, and pour it on the said swan flamingo while turning the spit so that the paste cooks on it, and be careful that no wings or thighs be broken, and put the swan's flamingo's neck as though it were swimming in water, and to keep it in this position, you must put a skewer in its head which will rest between the two wings, passing all other, until it holds the neck firm, and another skewer below the wings, and another between the thighs, and another close to the feet and at each foot three to spread the foot: and when it is well cooked and well gilded with the paste, take out the skewers, except that in the neck, then make a terrace of whole-wheat pastry, which should be thick and strong, and which is one fist thick, made with nice fluting all around, and let it be two feet long, and a foot and a half broad, or a little more, then cook it without boiling, and have it painted green like a grassy meadow, and gild your swan flamingo with a skin of silver, except for about two fingers width around the neck, which is not gilded, and the beak and the feet, then have a flying cloak, which should be of crimson sendal on the inside, and emblazon the top of said cloak with whatever arms you wish, and around the swan flamingo have banners, the sticks two and a half feet long with banners of sendal, emblazon with whatever arms you wish, and put all in a dish the size and shape of the terrace, and present it to whomever you wish.