Overlay one of your doilies on top of
your flag, and pin it in place. Despite how it's pinned
in the main picture, I actually found it easier to
stitch from the underside, since you can see your seam
line much easier, so you may want to pin from the back.
Yeah yeah, do what I say not what I do. You know the
Once you have it pinned, stick it under
your machine and using matching thread, sew a seam along
the edges, stitching the doily in place. I'd keep going
all the way around the flag, to keep the edges from
fraying too far. Once you've gone around the edges, you
may also want to add a few small seams along the doily
center, to keep it tacked flat to the flag.