"ancient Roman priest," 1530s, from Latin flamen "a priest of one deity," which is of unknown origin, perhaps from PIE root *bhlad- "to worship" (source also of Gothic blotan, Old English blotan "to sacrifice"). Also used from early 14c., in imitation of Geoffrey of Monmouth, in reference to ancient pre-Christian British priests. Related: Flamineous.
The old connection of flamen with Skt. brahman- is highly problematic, and has been dismissed by Schrijver. As WH surmise, the ending -en points to an archaism, probably a n[euter] noun "sacrificial act" which changed its semantics to 'priest'; for a similar shift, cf. augur "bird-observer" .... The only viable comparanda are found in [Germanic], but they show root-final (or suffixal) *-d~. [de Vaan]
Transitive meaning "to burn, set on fire" is from 1580s. Meaning "break out in violence of passion" is from 1540s; the sense of "unleash invective on a computer network" is from 1980s. Related: Flamed; flaming. To flame out, in reference to jet engines, is from 1950.
1882, from Spanish flamenco, first used of Gypsy dancing in Andalusia. The word in Spanish meant "a Fleming, native of Flanders" (Dutch Vlaming) and also "flamingo." Speculations are varied and colorful about the connection between the bird, the people, and the gypsy dance of Andalusia.
Spain ruled Flanders for many years in 16c., and King Carlos I brought with him to Madrid an entire Flemish court. One etymology suggests the dance was so called from the bright costumes and energetic movements, which the Spanish associated with Flanders; another is that Spaniards, especially Andalusians, like to name things by their opposites, and because the Flemish were tall and blond and the gypsies short and dark, the gypsies were called "Flemish;" others hold that flamenco was the general Spanish word for all foreigners, gypsies included; or that Flemish noblemen, bored with court life, took to slumming among the gypsies. Compare Gypsy.