`Lucky I will try to explain. I sewed my circles in "blocks" with 4 circles in each block. I added the flannel, then ironed down the "flaps" I found that I could sew the inside flaps down and stitch around them all without starting and stopping just sewing continuous. That would probably be better explained with a picture :( once the 4 circles were made into blocks I sewed the straight seam to connect them, then fold down the flaps and ironed then do the zig zag stitch as I joined the rows. when joining rows sew your straight seam iron your flaps down put the row you are adding to the inside of the machine and zig zag down the length of the connected rows. (Here is where I was making it harder on myself I'd turn the quilt around and try to shove the big part through the little opening) *Easier way is to go back to the top and start zig zagging down the other side of your flaps so one time you will start sewing on the left hand side of your joined rows and the next time you will start sewing on the right hand side of the rows. I hope this makes sense, if not let me know and I will give it another try to get it right.
I am not sure how you would make it with the raggedy edges - maybe sew further in on the flaps so they fringe?