No, priority mail is not just flat rate service. It is an expedited shipping service with (nowadays) full tracking and faster delivery than parcel post. I ship about 1000 packages via USPS priority every year.
You CAN use flat-rate boxes from the USPS to ship priority if you want to. The boxes are available at no additional cost -- you are paying for the boxes as part of your priority mail fees. There are three basic flat rate boxes -- small, medium and large. If you ship APO/FPO (in other words, ship to a military address), there are APO/FPO flat rate boxes too.
From Iowa (or Chicago), Priority flat rate may be more economical if shipping heavy packages (more than about 3 lb) to either coast and if the product fits in a flat-rate box. If shipping to the central part of the US or shipping lightweight orders to the coasts, however, regular Priority is almost always less expensive.
There are non-flat-rate Priority mail boxes too -- again, there is no additional cost for the boxes. Just ask for them at your PO.