I made one regular quilt with Minky and the cut edges just 'shredded' in small pieces--it did not ravel or fringe like cotton or flannel. So I suggest you take a test square of your Minky, cut the edges like you plan to do on the rag quilt, wash it and see what happens. You sure don't want to do all the work assembling a quilt and then Find out the minky does not give you the look you want. Oh and I second the advice about prewashing the flannel as it can shrink a lot and unevenly.