I have snowkited without bindings. It was a riot! I fashioned a Noboard out of a old snowboard I had lying around. I used furniture leg protectors from the dollar store as a big grip pad (the sticky foam circles you put on chair legs to protect the floor). I also mounted a old bike tube as the rope. However, I only use the rope for riding the mountain. Noboarding is super fun if you haven't tried it yet.
Just like noboarding on the hill, this setup only works in powder. It's absolutely useless on hardpack and ice as you cant get strong edge leverage. I have been looking at powder skates with a bi-deck to overcome this challenge. I have seen videos of guys riding the Peak chair at Whistler quite successfully with those things and it looks like a great setup for kiting with. Check it out
http://snowskaters.net/videos/287/powskating-the-peak