The Duke of Sandringham only appears in one chapter, although we hear about him at the beginning, specifically that he's a presumed Jacobite and employing Jonathan Randall in some capacity. As a result of this foreshadowing, Claire (and the readers) thinks that he's going to be a villain.
So when she encounters this "bluff, hearty, red-faced sportsman" (24.586), she's surprised to find that she likes him. Sure, he's a sodomite who tried to take advantage of Jamie when he was young, but he's also friendly, not predatory like Jonathan Randall. He amiably flirts with Jamie, but not in a way that puts his life—or his virtue—in danger. We have to wonder if this man, and his sketchy politics, will come into play in later books in the series.