A cold water wash minimizes the shrinking that takes place during washing. In my experience, the most shrinkage occurs when drying in a high temp dryer. So, your plan to wash in cold water and lay flat to air dry should cause very little shrinkage (maybe 1%). Hot water wash and regular dryer will cause about 3% shrinkage in an 80/20 batting.
When you lay out flat to dry, putting a fan or two on the quilt will speed drying as will turning the quilt over periodically. Once most of the water is out of the quilt, you can finish drying by hanging on a stairwell or the like (which allows air to both sides).