FLAIR is only a noun. It can mean either (1) distinctive elegance or style, or (2) a natural talent or aptitude.
FLARE as a noun means (1) a brief blaze of light; (2) a sudden outburst; and (3) an expanding or outward opening.
FLARE as a verb means (1) to blaze with sudden, bright light; (2) to burst out in anger; and (3) to expand or open outward.
As you can see, the verb and noun are closely related.
“He has a natural FLAIR for carpentry.” (noun)
“The carnival featured food with a European FLAIR.” (noun)
“There was a FLARE of light as the campfire was lit.” (noun)
“Bell-bottom jeans FLARE out at the bottom.” (verb)
“Tempers FLARED at the staff meeting this morning.” (verb)
TIP: flAIR means a certain “AIR” about you. It’s always a noun. FLARE can be a noun or a verb, but if it’s a verb you want for your sentence, use FLARE.