Hi and welcome from North Carolina!
I can't help with your Minky questions because I've never used it, but I can tell you about flannel. Tesspug is right on. It shrinks and frays and some is off grain. I make receiving blankets for infants out of it, but I really don't like it for backing quilts. Fleece is even worse from my experience. From what I've heard here on QB, Minky may work better for you.