I play a male Consular and have barely been able to Flirt with anyone.
I guess, more so than even Jedi Knight, the Consulars are not much when it comes to romance options. As I read so far, Consular male can only have 1 in-crew romance while female can have 2? So you choose the right gender actually.
If you want to flirt with every female in sight, try Sith Warrior male.
Every female quest giver I've come across has given me some form of Flirting option.
And you get Vette and Jaesa. It's almost like the devs want everyone to be a male SW.