Everyone knows about those beautiful birds called flamingos. One
sees them in zoos and parks and in the wild. They are not the oldest
birds to inhabit this planet, but they have been in existence for a
while. The oldest fossils of flamingos (i.e. prototypes) are
apparently ones found in the Green River Formation of Wyoming. These
are from the middle of the Eocene period (54-38 million years ago).
The specimens are aroun 46 million years old. A fossil species found
in this locale is called Presbyornis pervetus Wetmore. The genus
Presbyornis is believed to be the common ancestor of flamingos and
ducks. Presbyornis lived during the Maastrichtian (71-65 million
years ago), which was the last subperiod of the Cretaceous, and
through the Paleocene and early Eocene. The species Presbyornis
pervetus Wetmore is apparently closely related to a South American
Eocene bird called Telmabates antiquus Howard. T. antiquus Howard is
closely akin to a bird called Telemabates howardae Cracraft.
Flamingo fossils dating to the Oligocene (38-26 million years ago)
and the Miocene (26-7 million years ago) have been found in France.
The species of these deposits include:

Phoenicopterus elornis
P. agnopterus
P. croizeti

Phoenicopterus ruber is a living species of flamingo, but it goes
back a fairly long way. Fossils of it have been found that go back 4
million years; these are of the Pliocene.

Neal Robbins

P.S. This is the taxonomy of flamingos:

Kingdom: Animalia
Phylum: Chordata
Class: Aves
Order: Ciconiiformes
Family: Phoenicopteridae
Genus: Phoenicopterus

These are living species of flamingos:

Phoenicopterus ruber
P. chilensis
P. minor
P. andinus
P. jaesi