Firstly, loads of people repeat offend with exes. We break up because we know it's not going to work out in the long run. Initially there's a sense of relief, the pressure of "the relationship" comes off and suddenly the person who was a partner driving you nuts is now just an ex you still know really well but no longer have to put up with. Suddenly they look a lot more appealling again. It happens a lot and in no way does it mean you'll end up back together. But sooner or later one of you will move on and that's the end of it.
Secondly. People often stay in contact with exes immediately after breaking up. I think this is a bad idea. You develop habits in a relationship and those habits and behaviours can be hard to break. She might just be acting like that with you because she's always acted like that with you and doesn't know how else she should behave? It helps to get some space and perspective. I've told exes (after slipping back into old habits, and the sheets together) that we need to have no contact. At least for a good 6 weeks, maybe more. When we finally do get in touch with each other it's not the same relationship anymore. It's a new one based on frienship, not romantic behaviours.
And every anecdote I've heard of exes remaining friends (real friends and not just acquaintances who constantly gossip about their ex because they aren't really over it) has occurred after a break of 6 months or more.
Lastly, people are possessive in relationships. It's hard not to be. Plus your self-esteem can take a hit when you're single again even if it's you initiated the break up. It's a failed relationship. A failure. A common reaction for most people is to prove "they've still got it" so will flirt with their ex in an effort to make them jealous, or to get confirmation that despite the break up their ex still finds them attractive.
None of this is particularly weird, unusual, or illogical. In fact it's often the norm when you're young (assuming you are young). If you're happy the relationship is over and don't want her mixed messages then tell her straight. If you're happy to have the flirting but don't want anything more then be careful. You might find yourself with your defenses down and either sleep with her when you didn't want to. Or worse you start getting comfortable in this pattern and she suddenly turns up with her new boyfriend. You'll feel hurt and betrayed and she'll just say "But why? We broke up months ago?"
Good luck.
