I have made several rag quilts for my family and as gifts. I have never had one come undone. I like using flannel because the edges rag up so fluffy. I have used 100% cotton with flannel in between for the batting.
When I am short on money for batting, I bought a $4 blanket from Walmart and tused it for the batting. It was just as soft as the ones I used Warm and Natural on.
Another tip is about scissors. Heritage cutlery makes a pair of scissors just for rag quilting. They cut like a knife through warm butter and do not cause stress at all to your poor hands. I love mine.