Do the snowflakes have to be flannel as well? To me, it would make sense to do them with a more tightly woven fabric. Felted wool might also work for the flakes, allowing you to do machine buttonhole edges, or even a simple top stitch leaving the edges to fringe.
BTW, Yes, cut freezer paper works well in the copier or you can make of stack (stapled or lightly ironed where it won't hurt) and cut several at once.