The aerodynamics of vehicles with flat, squared-off backs are such that the air swirls around back there and dust and stuff is all stirred up and some collects on the vehicle. I don't think there's much you can do to eliminate it. The mud flaps (and also the "hula skirts") are more intended to cut down on stones that get kicked up and similar things; I don't think they do much to keep the back of the vehicle cleaner.
I have a hula skirt, and carried a bicycle on a receiver rack to, from, and around Alaska. It got plenty dirty. Indeed, particularly on the Dalton highway, absolutely everything anywhere on the outside of the RV got plenty dirty; all the Nike swoop-like graphics were pretty much invisible upon getting back to Fairbanks. It was well worth the dirt and wear and tear to experience the beauty of the arctic.