I don't mean to have M just drag you along. I mean ask her to turn you into her socializing experiment.
"M, your flirtation skills are legendary. I want to be your grasshopper and have you teach me the ways of snatching the pebble from your hand. I'm a dude, so your work is cut out for you, but I bet you could do it. No picking up smouldering urns with my bare wrists though."
Hell, turn it into a game. Hang out with her and have her pick out a chick to hit on. Go hit on her, and report your results.
Or you could try something perhaps more sane (maybe)... hit on your cashier. No, really, next time you go to the grocery or a restaurant, look at your cashier or waitress. Find something about her that sticks out (something, not somethingS, sheesh). Make a comment about it like a normal, not creepy person. ("Hey, Cindy, let me ask you... Is it true that I should avoid the crab delight at all costs?" or "Hey there, Sue, you look like you're ready for this shift to be over.") It's good practice at using her name and working on being more fluid. It doesn't matter if she's 18 or 80--it's practice. Think: Southern charm.