Make two sleeves and sew them to the two sides that are closest to the top. Leave a small gap (no more than 4" total) in the middle at the center - the very top.
Make a V shape using two dowels and miter join them at the top (use flat dowels it's easier). Remove the hanger part of a wooden hanger (they unscrew from the wood) and screw it to the top where the V dowels meet. At this point you can probably fashion any type of "hanger" as it will be partially visible you'll want something "pretty". Or even fasten a flat picture hanger hinge to the peak and use that.
If you want to lay REALLY flat, make two more sleeves for the bottom to sides, but don't leave a gap. Just insert dowels into the sleeves as 'weight' so it doesn't flop. Just make sure whatever kind of hanger you use will support the weight of all 4 dowels and the quilt.