The old silk may be so fragile that any attempt to sew it would shatter the threads of the weave. If it is anything like the old silk falgs I have framed, my guess is that it would not withstand any amount of stress.
I suggest using a fine mesh fabric overlay mount using Stabilitex (polyester) or Crepeline (French silk organdy) fine mesh fabrics, which are almost invisible in applications like this.
Cover a sturdy board with polyfill to give it a slightly springy loft, and cover that with a chemically neutral, color fast fabric.
Lay the flag on the lofted background fabric, and overlay a piece of Stabilitex or Crepeline to cover it. Pull the overlay tight enough to slightly compress the polyfill and create slight pressure between the background fabric and the overlay fabric -- that's what supports the flag and holds it gently in place. Fasten the edges of the fine mesh overlay on the back of the mount board. For more on this technique, see the May, 2005 issue of Picture Framing Magazine, page 49.