Okay so the thing that's bothering you is that she accepted the compliment and it didn't make her uncomfortable? Or do you think she's cheating? I think if it's the first thing that's fair, did you say that to her? In the moment what could she have done differently, and what could she do now to make you feel better about it? Is there actually anything specific you think would help or do you not think you can get past this?

I'm not trying to tell you you're wrong btw it just doesn't sound to me like you've really thought through what you actually want here. I don't think it's unreasonable for it to bother you that she seemed into it, I'm just not sure what that gets you besides feeling like you're right here and she's wrong. You need to figure out why exactly this bothered you and what you want from her now that it's happened for you to feel like the issue is resolved, and then bring that to her and see what she says. If she's like "oh my bad, I can see why that upset you here's how I'll do it differently next time" and that's good enough for you you have no more problems, but if she's unwilling to do anything differently and this really bothers you, you have your answer. Good luck my guy

I mean what do you mean "is it alright?" Like was he out of pocket or flirting with her? Probably. Is she in control of what this guy thinks or says? Not really.

Like are you asking if you get to be mad at her, or mad at him, or what? I don't think you can conclude that there's anything going on between the two of them just for that but I would be side eyeing the guy pretty hard. I know I wouldn't say that to a woman I knew had a partner myself. But whether that has anything to do with her is another question entirely