Now, I'm not naive enough to believe all women are great at flirting - I'm sure there are one or two out there who can't do it (although I've never met them - and those who say they 'can't flirt' are actually the best at it!). But if you have a strength, like flirting, and you are also a woman... then you need to find ways to use that to your advantage in a business setting - to get your project budgets approved, who influence decisions in the way you feel they should go, to get that cute guy in marketing to go out with you (just kidding on the last one!). Bottom line, use your strengths when negotiating, and don't feel bad about it.
Think about it. I'm a guy (arguable, but true), and if I flirt it just becomes creepy! It's not a strength I have, plus the above research shows it's probably not a good negotiating skill for me to use as a male. But I love sports, and in a heartbeat I'll sway an entire conversation during negotiation to talking about the other parties favorite teams, players, etc. Set up future times to see a game and grab a beer, send over tickets to the next big contest, etc. I'm a guy, it's what we do - it's a strength.
So, women, especially those in HR - get your flirt on - embrace it, have fun with it - see how far you can push the envelope with it. It's a skill - and one that your male counterparts usually aren't very good at. Just think about how many drinks you've bought for a guy vs. how many drinks have been bought for you. That's all just a negotiation - of which I'm usually on the losing end (okay, always on the losing end!).
I know some women who get their way around negotiating tables with a little bit of flirting. It works, they swear by it.