Flair and Flare

Flair is a noun referring to a natural talent (she has a flair for languages) or a distinctive elegance (he dressed with flair).

Flare can be a noun or a verb.  As a noun it can refer to a fire or a flame, or something you would ignite to make a signal light.  A solar flare is an area of intense activity on the Sun.  In photography or videography a flare is light reflected between lenses.

As a verb, flare can mean a sudden increase in a fire or flame.  Flaring can also refer to spreading outward.  Twirling will cause a skirt to flare out.