Repairing a rip in my hvac vent
You'll have a hard time getting foil tape to bond there, I think, and that component is designed to be flexible, partly for noise abatement. Foil would probably fail before long.

I'd cut a patch of heavy fabric (maybe marine vinyl) and bond it with a flexible adhesive--maybe 100% silicone. Clean the area and let it dry thoroughly first. Silicone would be set up enough to use in a couple hours. If there isn't too much movement when the furnace is running, the heat will speed things along. You could temporarily pad the patch with some soft foam or cloth secured with tape to hold the patch in place. 

If the fabric is sound, and it's just a seam that has let loose, a little needlework might do as well.