Flirting for me can be summed up in two words:
eye tag .
It's usually used with people you don't know, may never get to know, and don't care either way. It's not even a way to flirt yourself into a desired scenario. But it works for me, because at heart I am a wallflower and not seeking anyone at this point to get involved with even on a shallow level. I should say it worked for me (past tense), since I no longer go out in public much to make use of it. I used it more as a way to prove to myself that people were looking at me with interest, that they were paying attention .
I'd go into a bar or coffee shop and sit facing the largest open area, my back to a wall . There's usually numerous stimuli outside human targets, i.e. TV's, jukeboxes, live bands, or the hum/whirr/hiss of the blender/espresso machine/frother to focus on and shift from, point to point to point, so that you never look like you're staring , but merely scanning the room.
If you have good peripheral vision as I do, you may catch your mark giving you a once over, or scanning the room himself. The goal is to preface your eye contact with a mild body movement that is in itself natural (a shift in cross-legged position to knees together, or tapping the ash on your cigarette), then point your eyes like a beam and slowly drag them across until they hit their mark. Boom.
In a split second, none of his face exists outside his eyes . All you want to see are his pupils pointed right back into your own. Not down at your body, or over your head, or through you, but back at you, where your eyes started from. You'll be lucky if you can manage to smile or do anything, because none of that matters right now. If you smile when you don't want to, or ask for more than the look, you will have ruined a very good and cleanly executed exchange of eye tag .
So, anyway, that's how I would do it.