If I were going to make a pieced quilt from flannel, I would definitely wash and dry it. I just made flannel PJ's for Christmas and some of the yardage shrank from 45 inches wide to 39 inches. I'm glad I always buy extra for "pattern alterations", etc. I'm thankful I washed BEFORE cutting. Otherwise nothing would have fit in the end.
Every manufacturer's flannel seems to shrink at a different rate. Not all flannels are equal and sometimes the best way to make sure your fabrics will "work" together is to prewash. Of course, I advocate prewashing everything.
If I wanted to use flannel to back a cotton pieced quilt, I would definitely prewash because they shrink at different rates. I may be pickier than others but I want things to lay flat, be square and look right.
Those who use flannel for rag quilts seem to prefer not to prewash because they like the raggy look. That's not something I'm into so I'm sure there are better reasons for not washing in this situation.