easy fix
dab some good clear silicone on the burn holes and let it cure
And if a swab of silicone caulk won't cover the hole, then just clean the area with alcohol and lay it out on a flat area and silicone another piece of silnylon over the hole. I always use Permatex Flowable Windshield Sealant, same as I use to seal seams. Best to have something heavy to sit on top of the patch.
