Etymology of Flamingo and Flamboyant
The word flamingo and flamboyant share the same root. Both came from “flame”. Flamingo is flame-like bird. Flamboyant is flame-like look, behavior.
see that flamboyant guy in flamingo feathers? His name is Donquixote Doflamingo.
[etymology of flamingo https://www.etymonline.com/word/flamingo]
long-legged, long-necked brightly colored pink bird of the tropical Americas, 1560s, from Portuguese flamengo, Spanish flamengo, literally “flame-colored” (compare Greek phoinikopteros “flamingo,” literally “red-feathered”), from Provençal flamenc, from flama “flame” (see flame (n.)) + Germanic suffix -enc “-ing, belonging to.” Perhaps accommodated to words for Fleming (see flamenco).
[etymology of flamboyant https://www.etymonline.com/word/flamboyant]
1832, originally in reference to a 15c.-16c. architectural style with wavy, flame-like curves, from French flamboyant “flaming, wavy,” present participle of flamboyer “to flame,” from Old French flamboiier “to flame, flare, blaze, glow, shine” (12c.), from flambe “a flame, flame of love,” from flamble, variant of flamme, from Latin flammula “little flame” (see flame (n.)). Extended sense of “showy, ornate” is from 1879. Related: Flamboyantly.