This order is represented by a single family, Phoenicopteridae (flamingos).
References
Torres, C.R., L.M. Ogawa, M.A.F. Gillingham, B. Ferrari, and M. van Tuinen (2014), A multi-locus inference of the evolutionary diversification of extant
flamingos (Phoenicopteridae), BMC Evol. Biol. 14:36. (pdf)