Any old propane torch will do. I used to clear ditches with one.
Couple things though.
You have to get back to the same spot repeatedly to get some of the weeds, but after a season of getting at them repeatedly they are gone.
Be fire safe using it! At least have another person nearby knowing you're using it. A hose or 2 handy in case something does catch. Not on a windy dry day.
I hear tell the galvanizing on chain link fencing can actually make very harmful fumes if it gets hot enough. Just be sure you can't smell it I guess, or try not to make it that hot directly on it.
A propane torch has a lot more uses of course than just burning weeds. Helps light a not optimally dry burn pile. Can scare a bear away...
Forgot how taxing burning is. That is all I did Saturday. Ditch bank, ditches, by wet hole, etc. I hurt Sunday. Faithful dog slept all night Saturday and too tired to play Sunday. 2 good things, weeds gone, dog whipped.
Only bad thing, laid coat down by papers I was using to spread fires, caught on fire.