Never flirt with women because the majority of reasons why women flirt is not because they find you attractive, it's because they want something from you.
When you barely get attention from women, it's hard to tell the difference between the types of attention that women give to you and that's why I never recommend flirting with them.
I don't care if she's touching you or telling you you're hot, you don't flirt with her back. What I say don't flirt back, what I mean is don't get feminine with her and don't try to charm her. If she tries to flirt, try to be formal. The energy of authority is what you want to give off. If a woman flirts with you, don't flirt back, just take action and ask her out.
Just don't flirt with her back because flirting with her back shows interest. It's much better to make her feel that she's doing all the flirting. By flirting with them, you're essentially validating them so don't flirt with them.
Some women would get frustrated at the fact that you're not flirting back with them and that's good because if they get frustrated they might try harder and be more direct. Just don't over pursue them because some women just love the power that their charm gives them.
Nonreactiveness turns women on because it feels that they have to do more to get the reaction that she could easily get at another guy.