It's actually an interesting question.
If we don't get into the discussion of "he's not confident, hiding under a mask, etc." since everyone has a different opinion on this, we can look at some points of the game:
1. Ast only agrees to a poly relationship with Halsin, no one else Tav will share with. In turn, Halsin after defeating the brain tells Tav "for now" the affair is over. Perhaps Halsin is not seen by Ast as something long term.
2. Ast says of relationship Tav with Halsin (by implication, can't remember verbatim) that he regards it as a natural need, like for him to bite someone, and he has no right to limit you from doing so. Also, Halsin always pops up before completing a personal quest while Ast and your character are...um...observing a "hunger strike".
3. His attitude is also interestingly discussed by Shadowheart if you find yourself in a love triangle between him and her. On the suggestion of sharing, she says that "you overestimate his ability to share. He may seem like a carefree hedonist, but he's actually fragile if you can give him the comfort he needs."
4. The scene with the drow can be considered that having completed his personal quest, he finally wants to experience something of his own volition. (Although it doesn't lead to anything good for him, it's his decision and If a player initiates a trip to a brothel). He doesn't ask for it himself. If we goes to the brothel before completing the quest, he will refuse to participate, and will say something along the lines of: "Elven prostitutes, again".
5. For Mizora, Spavn swears. AA kinda doesn't, but then again, who sees what. Some see his reaction as just another mask.
6. For Harlep, both don't seem to swear. He say: "What you're doing, he can't be trusted". But there wasn't even a reaction to it before either.
7. The girl in the sewer. Honestly, in all my playthroughs, I've never once seen him flirt with her. He makes jokes about her.
You can catch disapproval from him if you say she was lured by a vampire. But he doesn't flirt. So, for me, in my games, there was never any flirting with her and I can't judge on that.
He's flirting in Act 1 with Shadowheart. With Laezelle. With Will, reminisces, "about bathing young in a fountain" (whatever that means), but that's Act 1.
I may have forgotten something else, but that's all I remember from the game so far. In my opinion (just my opinion, I don't insist) he's more of a monogamous guy, with "possible" digressions. Like he said, "I just like to have fun, what's wrong with that?". He's not as adamant as Laezel, or Mintara. Anyway, these ladies explicitly say no. Long term? Well that's in everyone's head). In my head is more yes. But that's just my preference, I'm just not a poly supporter.
In the game, characters can take any shape and gender: dwarf, dragon, elf, tiefling, halfling, drow, gitianki and ...human, what is not diversity, if you know what I mean?))))))
Though I've encountered another opinion that those who support poly were unhappy that Ast didn't turn out as obvious as the same Halsin. But they categorize Ast as poly.