I think the best option is to make the quilt without pre-washing. This sounds contradictory because I am normally a pre-washer, I have had flannel that shed a lot of dye in the wash, and I have had flannel that shrank very unevenly. Some of it has been cheap flannel, but some of it has been the "good stuff". Still, I would not want to pre-wash flannel pre-cuts. (I would pre-wash it if it were yardage, even FQs.)
When I make a rag quilt I use 3 layers of flannel and no batting. In your case, the center layer could be white or grey or lavender - whatever color blends with your flannel pre-cuts. That way there's no quilting necessary, because the 3 layers are sewn together and have no chance to shift around. Even if some of the flannels shrink unevenly when the quilt is first washed, I don't think that would be a problem with a rag quilt. Use some color catchers in case any of the fabrics bleed.