Two Rolling hitches or a Prusik loop done with flexible cord approx 1/3 the stay diameter will hold reliably on 1x19 wire. Pop the toggle at the top corner through the loop and push it up the stay to the desired height. A half hitch round the stay just below the flag holds it close to the stay, and if the tail is thin enough, two rolling hitches will hold the flag taut, otherwise use another Prusik to tie off to.
N.B. Take the Prusiks off the stay when you take the flag down when you leave the boat - you don't want a buildup of dirt excluding oxygen from the stainless surface as that can cause crevice corrosion.
P.S. If you clamp anything round a stay use Duralac to reduce the risk of corrosion.