Let me add my two cents..
Most women, decent women don't really give a shyt if you casually game other chicks in public. As long as it's not obvious, crude or leading to a BJ, etc.. in the fitting room.
Heck I sometimes do in front of my wife out in public when we're shopping, etc.., just for fun. Nothing serious and no kino, just seeing if I can spark some attraction and make somebody feel better than they would otherwise. She thinks it's funny to watch other girls reactions. I like to say when she takes me out in public, it's like she's walking her fancy poodle or something. Seems natural other women want to pet it occasionally. She knows that other women are going to look, and she knows that I being a friendly sort never miss an opportunity to communicate with other people especially very attractive ones of the female persuasion.
But she's 41 y.o. and quite mature. A younger woman could of course be a bit more insecure and possessive.
All that being said, there has to be a degree of trust in your relationship if you want a good one. That means if you have an understanding with your partner that you wont cheat, you shouldn't. Or you're liable to find yourself alone again doing it all for real again. If you can afford that, then by all means that's your decision. No reason to be deceptive about it.
CHAT
I believe that flirting is okay, as long as you don't act on stuff and cheat. I would just be honest to my LTR partner. But hey, all that matters is what you want to do.