To flirt means to show romantic or sexual interest in someone playfully or subtly, usually without serious intentions. In the context of the clue "Bat an eye, say," it suggests that flirting involves making subtle or flirty gestures such as winking or fluttering one's eyelashes in order to show interest in someone.
Note: The provided meaning of the answer is for the latest New York Times crossword puzzle clue: Bat an eye, say. Explanations are generated by AI and may be inaccurate.