Project status?
The cable would be inserted into the duct about 15’ away from the furnace plenum.
I assume a straight shot through a 6" dia round supply duct to a ceiling mounted outlet vent register? (Naturally the ceiling register would be remove when installing a fish tape to pull in the data cable.)
Good luck if you first have to travel through a main supply duct to the tap off for the 6" dia round branch duct that feeds the ceiling register.
FWIW, I would recommend you purchase the data cable from Blue Jeans Cable. They will make you a cable cut to length and install RJ45 plugs on each end of the cable. Cable will then be tested to make sure it meets specs standards. Not just a wire mapping test.
Protect both connectors so they are not damaged during installation.