I do not think that you can call either of the two main characters flat in this story. There are too many layers to each character. Despite being a short story, both Rainsford and Zaroff are quite well developed and deep characters. If you must pick a flat character, then I would go with Zaroff's servant, Ivan. Even Zaroff admits that Ivan is simple and flat.
"Ivan is an incredibly strong fellow," remarked the general, "but he has the misfortune to be deaf and dumb. A simple fellow, but, I'm afraid, like all his race, a bit of a savage."
I would call Zaroff the round and static character. He's static, because he doesn't change at all throughout the story. He's committed to hunting men. He doesn't think anything is wrong with it, and he's not sorry that he loses to Rainsford.
The general made one of his deepest bows. "I see," he said. "Splendid! One of us is to furnish a repast for the hounds. The other will sleep in this very excellent bed. On guard, Rainsford." . . .
He sees the entire situation like he sees a game, and that remains constant throughout the story. He is a round character, because there is significant detail in the story that explains to the reader how he became the man that he is when the reader finally meets him. The reader might consider him sadistic and crazy, but at least the reader understands how he came to be this way.
Rainsford is the round and dynamic character. He's well developed throughout the story, but most importantly, the reader gets to see his attitudes regarding hunting prey and killing another human being change. When the story begins, Rainsford has zero consideration for what his prey might be thinking or feeling. Once he becomes the prey, though, he realizes what it actually means.