Spoiler
Yes, he is a green flag. He is a very gentleman and I love him... No The Duke doesn't believe that she is cheating him. Even when she try to convince him she is pregnant of Mikhail (because Herdin finds out she is with child). He gets jealous for sure, but he still believes that Asiel is her only true lover, and she cannot meet him for some reason. That in some way, it's true

he's gonna think she's cheating and betraying him isn't it, bdw is the guild master a good character?