Can't say specifically for the Flagstaff, but I had a 2007 F350 CC LB FX4 with 20" wheels and my 5er sat fine on it with 6" bed clearance. Now have a 2012 F350 CC LB FX4 with 20" wheels and still fine. The 5er sits just a very little nose high on the '12 but not enough to be a concern.
Had rails in the 2007. But they really were not a problem or nuisance. But the 2012 had factory hitch prep which has underbed mounts and does leave a flat bed. One is not better than the other as far as function. There are several hitch manufacturers that make the underbed mounts now so you do have a choice, B&W, Reese, and others.