I am thinking of using it as a lubricant for the fan belt that the exhaust duct of the draft chamber connects to, is there an appropriate type of lubricant?

The grease recommended for maintenance of fan belts (shafts) of draft chambers, including environmental concerns, is Suzuki Kikou's lubricant H1 Bellhammer Grease.
The above product is a very environmentally friendly grease with sufficient lubricating power.
For convenience, a spray can also be used.