We do carry furnace cement, by Rutland Fire and Clay company, in individual tubes. These can be viewed here:
Given the nature of your project, these caulking gun style tubes would probably be the most manageable to work with. I am guessing this unit is cast iron. If so, this type of furnace cement is the best for assembly.
The only 3/16" gasket material available is this product:
This is an ovalized stove window gasket, but it may suit your needs. Please let me know if I can assist you further.