Do you have a serger? I saw a denim quilt in which the squares were serged together wrong sides together (so the serged stitches were on the top) with red wooly nylon thread (a thick and stretchy thread). The serged seams were then sewn down flat with a sewing machine.
I think this could work well with corduroy too, especially in terms of keeping the edges confined so they don't "shed".
In order to make a flannel backing for the corduroy, I would just layer a square of flannel behind a square of corduroy and serge all edges together at the same time. In order to avoid slippage, you could secure the two layers with a machine stitch in the valley between two wales in the middle of the square (or sew an X in the square the way rag quilts are done) before serging.