Confusion of these two used to be common. "flair" is from a French word, referring to a hunting
dog's ability to discover game ;(or even truffles) and was used as a metaphor meaning a talent
for discovering tasteful new styles, etc.

flare
vi.
flared, flar4ing 5ME fleare < ?6
1 a) to blaze up with a sudden, bright light b) to burn unsteadily, as a flame whipped about by the wind
2 to burst out suddenly in anger, violence, etc.: often with up or out
3 to curve or spread outward, as the bell of a trumpet
vt.
1 to make flare
2 to signal with a flare


flair
n.
5ME, odor, fragrance < OFr < flairer, to emit an odor < LL flagrare, for L fragrare, to smell, reek < IE *bhrag3, prob. < base *bher3, to boil up > BARM, BREATH6
1 orig., sense of smell; hence, keen, natural discernment
2 a natural talent or ability; aptitude; knack
3 [Colloq.] a sense of what is stylish and striking; dash