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most of those flatbeds are made by same company, whether they go on a dodge, chevy, or ford, so you should be able to do it, but i couldn't tell you what has to be done to go from one to the other.
The mounting holes might not line up perfectly, but you can drill through the top of the c-channel frame only and then bolt through and it is "mounted".
Then just fenagle the wiring and you're good to go.
I have a friend with a chevy cab on a F350 crewcab frame with a dodge bed - all leftovers from other things that have gotten wrecked and he combined them for one running vehicle. It's titled as a chevy