"Epicures regard my tongue as tasty. But what if my tongue could sing?" -Martial, on flamingos.

The main reason (beyond the need for sustenance) why someone would eat any food in particular is because they find it delicious. But those who are at or aspire to be at an elevated social class have further considerations- they want to seek out expensive and exotic foods to demonstrate their status and refinement. Flamingos are native to Europe (among many places), but are far more commonly found in Africa- and that exoticism made them a luxury good for wealthy Romans.

But why the tongues in particular? There is no better description given than that they have "an especially nice taste"- according to the Roman gourmand Apicius (through Pliny). They were simply regarded as the tastiest part of an exotic animal, perfect for a fancy, over-the-top Roman cena, or dinner party. Unfortunately, there is no recipe that has survived for flamingo tongues, nor is it possible to find out how exactly they taste without committing a crime (as it is not legal, at least in the USA, to hunt flamingos). The best analogue might be duck tongues- another aquatic bird with a similarly omnivorous diet- which would mean that flamingo tongues are likely very rich, but also very greasy and possibly a bit fishy. Flamingos might therefore need a strongly flavored sauce to stand up the the flavors of the meat itself. For that at least, we do have a Roman recipe.

What happened to the rest of the animal? Although the tongues likely went to the fanciest diners, the rest of the bird was at least slightly more affordable. Apicius gives a recipe for flamingo that I will copy below, braised in a heavily seasoned, vinegar based sauce.

"Scald the flamingo, wash and dress it, put it in a pot, add water, salt, dill, and a little vinegar, to be parboiled. Finish cooking with a bunch of leeks and coriander, and some reduced must to give it color. In the mortar crush pepper, cumin, coriander, laser root, mint, rue, moisten with vinegar, add dates, and the fond of the braised bird, thicken, strain, cover the bird with the sauce and serve. Parrot is prepared in the same manner."

Two recipes here for the price of one, if you've been wondering how to prepare a parrot who just won't stop talking. Roman cuisine was dominated by these sorts of pungent sauces, which most often had a focus on sweet and sour flavors, in this case provided by dates and vinegar.