The words flair, flare sound the same but have different meanings and spellings. Why do flair, flare sound the same even though they are completely different words?
The answer is simple: flair, flare are homophones of the English language.
A natural talent or aptitude; a knack: a flair for interior decorating.
Instinctive discernment; keenness: a flair for the exotica.
Distinctive elegance or style: served us with flair.
To flame up with a bright, wavering light.
To burst into intense, sudden flame.
To erupt or intensify suddenly: Tempers flared at the meeting. His allergies flared up.
To become suddenly angry. Used with up: He flared up when she alluded to his financial difficulties.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.