Flare is a burst of flame or light, or a signaling device used to produce a burst of flame or light.
Flair a natural talent or facility, and is sometimes used to mean "flourish"
Quotation marks are used to denote attribution, a literal phrase, or to cast aspersions on the source of a statement or phrase. They never, ever denote emphasis.
To test if you're using them, replace them with attribution ("what he said was 'Modern flair'") or aspersion ("so-called 'modern flair'").
Professional editing for publication has a requisite knowledge and skill set.