How long were you two dating?

If staying in touch and the flirting is bothering you, keeping you from healing, or giving you some false hope, then you need to cut all contact with her.

If you're up to remaining as friends, then stay in touch, but don't flirt back.

She dumped you,she doesn't get to stay in touch,she made her decision.

Now its time for you to start no contact and disappear from her life,start healing and moving on.

How old are you, and why do you let her contact you when she wants to, and flirt with you?

Did she say WHY she dumped you? Sounds like she still wants some kind of relationship with you-even friendship OR she IS a player. You draw the line there. Not enough details, in the end. I know I had to tell a guy I could not date him because of his drinking. I loved everything else about him. He could have been the PERFECT best friend if he didn't drink so much. It made him gossip like a girl, quite argumentative, "black out", and have memory loss... especially very convenient memory loss in a "I never remember being with any other chick or at Hooters" kind of way. I would have loved to remain friends BUT relationships have to be 50/50 and not enticing one or the other to be an enabler or player. That is a dangerous game.