There must be a zillion recordings of this. I guess the best-known must be the one by Duke Ellington. I can't find it in my CD collection, but it is in the Hal Leonard jazz fakebook.

Flamingo
(lyrics by Ed Anderson; music by Ted Grouya, 1941)

Flamingo, like a flame in the sky,
Flying over the island to my lover nearby.

[CHORUS]
The wind sings a song to you as you go,
A song that I hear below the murmuring palms.
Flamingo, when the sun meets the sea,
Say farewell to my lover and hasten to me.

Flamingo, in your tropical hue,
Speak of passion undying and a love that is true.
[CHORUS]