A rich, white male is usually referred to as a "douchebag" when they are particularly obnoxious and self-centered. it is a pretty strong word. "Preppie" refers to a particular style that emphasizes wealth and can be ostentatious.
If it is just that they are too showy then they might be called a "fop", "dandy", or a "popinjay" (these terms seems a bit old, but they can be used ironically and are kind of fun). They are not necessarily offensive, just terms to point out that a man spends a lot of time on his appearance and is what we call "flashy".