Just coming in here to say that I've beaten the prologue, and I've gone into the Hinterlands. Before that, I was talking to everyone, and I was shocked to see that even as a female you can flirt with Cassandra. She doesn't even react badly at all.
I'm wondering whether you can flirt with all romance options regardless of what gender or race you are? If so, that's pretty great.
Not Solas or Blackwall, which have no flirts whatsoever unless they are available to you. Cullen has very limited options which cut off in Haven fast (as in, the second flirt is your last flirt)
Makes we wonder if race-gated Solas would have expressed interest in other Inqis if only ever ignored his expectations and flirted with him.
And why couldn't we? Why couldn't my Inqi who OWED SOLAS their LIFE during the prologue promise to protect him just because he was a dwarf? (And also a man?)
I like hearing positive thoughts about the romances from other Aces, as it tends to reassure me that I'll enjoy them too. 
Does anyone else love the various reactions to flirting? Josephine seems oblivious (although I only got to flirt with her once), Solas seems flustered, and Cassandra just goes with it like, "Yeah, I'm a force of nature." I just think it's neat.
Cass, Sera, and Dorian all have full flirts if they're out of your pool, iirc (excluding the ones that are responses to their flirts, like "how pretty are you").
Cass takes them pretty much the same, as compliments (w/ cute smiles!)...
...and Sera mostly ignores them or says something cheeky. (Unless you're an elf. She doesn't like elves. Romancing her as an elf is incredibly difficult, esp. compared to qunari.)
Dorian sees it as a game and will flirt madly back, which is great.
Bull and Josie are obv available for anyone regardless of their CC options, so there's no such thing as incompatible flirts 
As for Blackwall, what you say on the battlements (you'll know what that means when you get there) is what locks him. If you DON'T take the flirt there, he is no longer in the dating pool and you lose all flirts. If you DO take it, he is the ONLY one in the dating pool (also known as "locked in"). All other flirts (eg: charming, admiring) are safe.
It's interesting that some of the "flirts" in this game are actually more about expressing respect or just a bit of humor and not "let's do the mattress mambo until the bed breaks down". I'm of two minds about that. On one hand, I guess it helps if you want to test the waters with a character without coming on too heavy, especially if going for an asexual relationship. On the other hand, these "flirts" are so non-flirty that it feels weird when they are treated as an expression of sexual/romantic interest and not simply as friendly banter.
I felt like some of those so-called 'flirts' made for better lines than the others, like telling Cass she can do anything she wants to, or complimenting Dorian instead of just brushing him off or insulting him.
...but then, I've always seem the 'flirts' as two-way street. The heart doesn't always mean you flirting with them, it's a 'warning' icon that means you're opening a path into romance territory. I see it as a way of them warming up to you, because you're so damn charming/supportive/cute.