I know a guy who added a gooseneck to a flat/dump, cut a hole in the middle of the bed, added a flap door, welded the hitch to the frame of the truck (I think he did) and he was good to go. If he didn't weld it to the truck frame, I wouldn't want to be around when the trailer and bed broke loose (dump bed with 3-4 points of contact to the truck). I have two flat/dumps and really don't have a desire to cut holes in the beds for bulky material to sift thru. I would like to have a gooseneck trailer but will settle for bumper pull trailers for now.
It shouldn't be too difficult to add a gooseneck hitch to a flat/dump, seems like you would have to jack the trailer up an extra 4"-6" to clear the bed, then drop it on the ball hitch.
Good Luck in whatever you decide!