The action of a flirt was a playful and lighthearted way of expressing romantic or sexual interest in someone.
In 2259 of the alternate reality, upon hearing Leonard McCoy's attempts to woo Carol Marcus on a planetoid where they were to examine an advanced long-range torpedo, James T. Kirk reminded the doctor that he was not there to flirt. (Star Trek Into Darkness)
(Star Trek IV: The Voyage Home)
In 2366, Youngblood was having a drink with Ensigns Darien Wallace and Bennett in Ten Forward when he was made aware by Bennett that a woman was looking at him. This was watched by Guinan and Lal; the El-Aurian explained to the android that this was called flirting. (TNG: "The Offspring")
(DS9: "The Ascent")
(DS9: "Afterimage")
(VOY: "The Killing Game, Part II")
(VOY: "Workforce, Part II")
(PIC: "The Star Gazer")
(LD: "Parth Ferengi's Heart Place")
(DIS: "Lagrange Point")