Flannel is a loose woven fabric (compared to your quilting cotton) which is why it shrinks up so bad. You will need to ensure it is washed at the very least the hottest temp the recipient is going to use. That way it will shrink as much as it needs to before you quilt it. Pre-washing is essential when using flannel
Minky is a polyester fabric. You do NOT need to pre-wash. If you do decide to pre-wash the minky, you need to finish the edges first. Either serge the edges or hem it. If you do not do that, your washer and dryer will be a stinking mess
polyester is not a woven fabric, it will shed horribly. It will not shrink, other than the parts that fall off in your machine.