Most of the flatbeds i've seen were like ScottG described.. 4xs running down the frame, and attached with monster U bolts.
Refer to the following image..
[img]
http://www.oldtruckstuff.com/woodbed.GIF[/img]
The red shapes are your 4x4's bolted to the frame
The green shapes are "stringers" (4x4's would make it rock solid) and run down the length of your bed
The yellow shapes are your actual floorboards for the bed, like 1x4 or 1x6's.. or plywood.. whatever you wanna use. (plywood warps and turns to crap when it gets wet, so I wouldn't use plywood)
You could then "box" it in all nice and pretty with some 2x6's attached to the ends of the "stringers".