If you get the flat rate box, you can stuff it full as you can for that rate. My post office used to have those tuffy bags, and I'm sure one quilt would fit in one of those.
my quilt is about 11x13x2 fold, which would fit in one of the tuffy bags.
You could probably go to the post office with you quilt/quilts not packaged and ask what would be the cheapest way to send it.