I think this woman suffers from a lack of confidence where needs to be constantly reassured that she is attractive to men. A somewhat harsh opening statement, but one from experience.

I had a relationship with a woman from work for a brief time. She was also one of these "flirty" women who was bright and cheery and needed attention. She was in fact already in a relationship which I had heard was on the rocks - I was the guy who she turned to when no was was giving her the attention she felt she deserved. A fall back position so to speak.
I was too blind with what I thought was love at the time to see what was happening in front of me.

From what you've described her relationships in the past seem to be destructive from the outset, as if she doesn't know what she's looking for in a relationship.

I think the only thing you can do is be her friend and thats all. Any hope you have for a real relationship with her would be leading yourself on.

I hope this helps.
H.R.