I recently made a baby quilt using flannel on the front and one large piece of fleece for the back. It came out much better than I expected...the quilting on the fleece looks fabulous. I didn't notice a stretching or moving problem, but I'm a crazy pin baster so I don't run into that problem. There was a lot of fuzz and I just made it a point to clean it out more often. I bound it with flannel - machine stitched to the front, hand finished it to the back and was really pleased at how it turned out and how easy it was. I'm mustering up the courage to use minky next time...hope this helps.
Edited to add: I did not use any batting - just the flannel top and fleece backing.