For a flannel lining that is set in from the edge, I would probably fold under the flannel raw edges, pin very well to the blanket (to prevent shifting while you sew) and do a blanket stitch on it. If you don't want the stitching to show, do a slip stitch. If you want how-to for either of these, just ask.
OTN: my first attempt at any type of mitten - doing fingerless
Oh...and I'm heajames on Ravelry