If the knotweed has invaded your garden to the point where you can’t spray weedkiller for fear of ruining other plants, paint a glyphosate gel on the individual canes and leaves instead. Please note: The WHO considers glyphosate to be a probable human carcinogen. Its use is prohibited in some states and countries. Please check with your local laws and use caution if handling this chemical.
Keep plenty of water nearby to put out the fire, and practice fire safety to ensure no one gets hurt. Research and follow all local fire laws and regulations before burning yard waste. Burning is not allowed in all areas.
Do an Internet search to find a registered carrier and licensed landfill site near you.