She would probably reply "I can talk to whoever I want, however I want. If I flirt, it's okay because that's just how I am."
I would probably say "Well, but you realize this is actually hurting me and I feel disrespected."
And she would say "It's not personal, it's not you."
Talking to this other person, and carrying on as she does has a price.[/b] The price is her SO (me) is hurt, feels disrespected, and uncomfortable.
Knowing the cost and continuing means that my hurt feelings matter less to her than this other person. Ergo, I am less valuable to her than he is.
Re-read your very own words a few times... again I've live this crap. I've lived the I'm a flirt crap... no more, I'm done with it. It is very personal to your SO if that is a boundary of theirs.
I just wouldn't tuck tail and run, confront it and be prepared to walk. If for nothing else, yourself. You're probably not going to hear what you want to hear, but it's better to hear it as opposed to not IMO. Is this the sort of person you want to have a relationship with long term? Really?