I assume that you're doing the ruffled binding like a double-sided binding. Double sided binding has raw edges that you must turn under on both sides by pressing to the middle. If that's the case, it should be a 1/2" layered seam of Fabric A, doubled ruffle, Fabric B with the seam pressed open (Fabric A + one layer of ruffle going one direction and Fabric B + the other layer of ruffle going the opposite direction).
If your issue is that the fabric is fraying before you can get it enclosed, instead of burning encased raw edges, I'd do a pinked edge. Burned edges will add slightly more bulk and you already have 8 layers of fabric plus your batting in there so the last thing you want is any more bulk.
If the issue is that your entire satin binding is fraying after it's finished, in addition to the 1/2" seam, instead of finishing with a hand stitch or straight machine stitch, you might straight stitch the 1/2" on the back, flip & then machine stitch with a zig-zag or decorative stitch on the front. That's how I learned to attach satin binding to blankets; it is very secure and will last a long time without fraying even if you do nothing to the encased raw edges.
Gosh! So hard to explain without pictures. If I wasn't clear enough, let me know & I'll try to scan some illustrations in tomorrow night showing you what I mean.