Sadly most of the depiction of 'thopters in Dune media have not been 'thopters but boring generic VTOLs. I think the only place where they actually had real bird-like 'thopters was the Dune RTS games.
> I don't know any aircraft that propel themselves by moving wings.
Well, there are helicopters, of course, and—less common but more what you probably had in mind—ornithopters, both of which using moving—rotary in the first case, flapping in the second—wings.