(I'm a novice quilter, so take that into account.) I would match the flannel as closely as I could (or use a blender) and wash it several times to both fade it and shrink it. I'd replace the whole frayed piece and hand sew it over the old piece (I might try to remove it, I'm not sure until I see it). I'd either hand quilt or machine quilt over that piece to make sure it's stable and will last through another bunch of washings.
I definitely would not try to retire the quilt. Once it's your soft, snuggly quilt you've loved, you do not want it replaced with a stiff, sparkling new quilt. It's kind of like trying to replace grandma's soup with tacos.
bkay