bat (one's) eyelashes
To flirt with or feign romantic interest in someone, either by literally fluttering one's eyelashes or merely in general. Usually, but not exclusively, refers to women. She kept batting her eyelashes at me each time I talked to her, so I'm thinking of asking her out on a date. I like to bat my eyelashes at bartenders to see if I can get a drink or two for free.