I don't use cloth, but the one thing I bought that I can't live without with my chickens is a paper shredder.
I shed everything and since the paper is biodegradable if it gets knocked out it composts.
I do add hay to the paper lately, but they knock that out more than anything. I trying wood chips and other things, but the paper works. Costs me nothing really if you think about it and I even have someone who gives me their newspapers when they're done, so I have an endless supply. And a few pieces of paper makes a lot of shredded paper.
As for the cloth I would use some cheap canvas even maybe a piece of a feed bag. Leave it in one piece or cut it to shred it so they'll be able to get inside easily.
See how much I like shredding? LOL