Carpet generally can be installed without regard to the overall stability of the floor because carpet doesn't have any deflection or flexing issues. Since it can move with the camper as the camper moves (especially during transit when there are bumps and vibration from driving), so long as the subfloor and existing floor are in good shape you can put carpet right over the top.
Hardwood is a little less forgiving than carpet, but it still can handle flexing to some degree. Floating floors are not a good idea in a camper because they could potentially buckle up and pop apart during transit. However, if your subfloor and existing floor are in good condition, you can nail and glue hardwood down on top of the other material without worry.
You sometimes can tile over existing floors so long as you know the existing substrates are completely locked down and sturdy. However, you cannot use tile in a camper on top of an existing floor. Campers vibrate far too much for tile to be used, as it will crack and pop off the floor when the camper is moving. This issue is enhanced when the tile is laid on top of another surface, adding more vibration to the flooring.
Because vinyl is so flexible it is one of the most common flooring types used in campers. As long as the installation surface is flat, relatively smooth and in condition, you can apply a new layer of vinyl flooring without concern. Once everything is glued down and in place, the vinyl will move with the camper as it moves, leaving you with a flexible floor.