If I was one of the people who didn't use the kitchen I'd be politely telling you to go away if you tried to make me clean up other people's mess. As someone else said, you'll look very silly indeed if you actually try to enforce it. Have a word with your boss, and convince him that it's a stupid idea (and is he really so light on actual work that he has time to draw up a rota like that?).
If it's a genuine health hazard and you're too tied up in bureaucracy to make the cleaner do their job, then just get rid of the facility completely. tbh, even where people are cleaning after themselves it'll still need some proper cleaning done once in a while to keep it hygenic.