I'm pretty sure starting in 99 the 450's, 550's and all Chassis cab 350's had flat frame rails from the back of the cab back to the end of the frame unlike pickups which have a "kick up" over the axle on their frames. Additionally, your truck has a chassis cab industry standard 60" CA (Cab to Axle Centerline) measurement where as pickups have a 56" CA distance. This is why aftermarket flatbeds are typically 9 ft long because the frames are slightly longer. Furthermore chassis cab frame rails are spaced 34" apart from outside of the frame rails. Pick up frames are 38".
To get a dually bed to fit will require several things.
To make up the difference in chassis length for the dually pickup bed you can track down a set of filler panels like most of the aftermarket upfitters use when putting a pickup box of 450/550 chassis. It is a fiberglass panel that matches the body lines of the truck and attaches at the frong of the bed on both sides and blends in fairly well. This will allow you to fit the bumper to the end of the frame. Several companies build the conversion trucks like this. The only one I can think of right now is Manning Truck Equipment.
There is one company out there that takes a dually bed and actually shifts the dually fenders on the pickup box back 4 inches. This eliminates the need for the filler panels for a cleaner look, but it requires you to shorten the rear end of the frame by cutting it off to a length where the bumper will mate up properly for the right factory look. I have only seen this method in pictures and figured it out after studying pictures comparing the two methods. I like option 2 as it is a nicer finished appearance, but I do not know if you have to modify the bed sides when you shift the dually fenders back.
No matter which method you use you'll have to fabricate custom mounts to place the bed on the frame to achieve the proper height to match the bodylines from cab to bed.
Finally, where is your fuel tank located? If it is behind the axle you probably have to use the first method because the tank will prevent you from shortening the frame. If it is behind the axle you need to get all of the fuel filler door and filler neck pieces from a shortbed dually. On shortbed duallys the filler door had to be mounted in the front side of the dually fender. You have to use these pieces to mount your fuel door on the BACK side of the fender because that is where your fuel tank is located. That still leaves you with the factory fuel door at the front of the bed unused if you don't mind having a door to nowhere.
Then you have to figure out the wiring harness on your frame to match it with your pickup bed harness...