flutter (one's) eyelashes
To flirt with or feign romantic interest in someone. (Literally fluttering one's eyelashes is an exaggerated way of doing so.) Usually but not exclusively refers to women. She kept fluttering her eyelashes at me each time I talked to her, so I'm thinking of asking her out on a date. I like to flutter my eyelashes at bartenders to see if I can get a drink or two for free.
flutter your eyelashes
open and close your eyes rapidly in a coyly flirtatiousmanner.