From my limited experience, the woman I met enjoyed the jealousy game.
I figured she got multiple benefits out of it including:
1.) It left her feeling empowered (i.e., the upper hand in the relationship).
2.) If I reacted it re-affirmed she was valuable, worth being angry/fighting over. If I didn't react there was another benefit (more below).
3.) She might have taken some twisted pleasure in seeing me hurt (this may be related to #1, essentially someone who feels weak inside, hurting others makes some people feel stronger).
4.) She enjoyed (needed?) the affirmation of many others and was not necessarily always aware of the effect it had on me. Besides hey, if her and 20 fan members are enjoying her flirting, and I'm the only one who isn't, doesn't that suggest I have the problem? (yes I'm being sarcastic).
5.) Plus it's a great, and entirely 'innocent' test, where you can't win

What I mean is on some level I think those with HPD are always shopping for more validation, a better relationship, etc., so jealousy is one of those games where they can disavow any responsibility ('who me? i was just flirting, what's the big deal?') while at the same time testing, keeping one's options open, since either way you react you lose. If you feel jealous you lose (this makes you weak which leads to the person with HPD thinking they could be with someone stronger, like they are cause hey, if you were stronger you could handle them flirting with others, which is fun for them), and if you don't feel jealous you lose (this suggests you don't care, so the person with HPD could think hey, maybe I should be with someone else who wants me more?).
Of course long term jealousy games are fail because eventually we just stop caring, and want to salvage our own pride. Yet on some level that's what the person with HPD wants too. For us to abandon them, which re-affirms what they knew all along, we didn't really love them and someone else will. Like maybe one of the fans they've been flirting with (who don't care that they flirt, because they are not emotionally invested and just want the attention, and maybe a shot at sex).