It is a down bomber jacket. So it consists of a shell, down filling, and interior liner. It is fairly loose so I can manipulate a needle under the shell without unstitching the interior liner, especially if I add a satin leaf or flower.
At that size something like a satin stitch or long and short stitch should hold it together well.
I think this is the direction I want to go (maybe even add a lil satin leaf). My biggest concern is that there isn’t really any space right at the stitching that connects the pocket to the coat. I might cut the threads holding the pocket flap corner, add the satin sitch, then reattach the pocket flap corner.