I have cut out a number of rag quilts using the Accuquilt 8.5 inch rag square die. I made reversible squares cutting a double layer of flannel. (In TX this is usually heavy enough!) I was advised by Accuquilt Customer service that if I found it difficult to cut 2 layers of flannel, just to cut one at a time. Eventually
my roller actually locked and I HAD TO SEND IT IN. However I generally had no trouble cutting out double flannel and don't see why adding a single layer of cotton would make a difference. I have made a real friend in one of the Accuquilt customer service folks. They are very willing to help and answer any questions. Sometimes there is a lot of cleaning the die that is required between several cuts. I have read, but haven't tried to cut this down by covering the die with thin paper, like parchment or tissue paper, Good luck,