*Yes, two. For obvious reasons. Would be nice if they were only available to people wanting same-sex options (i.e. you've got a straight male but can't [Flirt] with this woman because she's a lesbian and has no interest in you what-so-ever, doesn't matter if you're on the Dark Council
The question here would be, why not allow the flirt, but have her turn you down? In fact, why not just give the flirt option and have lots of turn downs! "Awww...that's sweet of you...but I'm straight." (works in reverse too).