Yeah... dating sites don't work that way. I can think of two sites when you say flirts (AFF or True). With both of them, don't be a non-member and expect serious people to contact you first. It really doesn't work that way. Just like the dating scene, you have to show interest and invest emotionally (which usually translates into money).
AFF I don't think it matters, really. It's just sex and you're lucky if you find a committed relationship on there. It's a beauty when it happens though! :D
For True, people are on there FOR relationships, not just a booty call. With the flirts, they send out random stuff to people they match you with. So really, the ladies sending you flirts or those generated messages probably aren't interested, those are just required to complete the profile. But seriously, on sites specifically for dating (not just sex) you should show some initiative and pay up.