You might put it up on the center stand, but (assuming you are using a generic box trailer) I would nose it into a corner and park it diagonally before compressing the suspension and strapping it down.
The problem with the kickstand is two-fold: 1) It provides a pivot point for the bike to kick up if you hit a hole or bump, and 2) metal-on-metal or metal-on-wood it more slide-prone than using the tires and suspension to hold it still.
With all of that being said, there was a time or two when I had nothing but 8 ratchet straps and a whole lot of prayer holding a bike in the bed of my truck. *I* wouldn't tow it that way, but it's not like it's never been done before.