what requirements does your house insurance require?
This is a good one to spend money on a pro installation - paying for the knowledge to have it done correctly will be worth it in the long run. As bad as any of us like to ask for help.
I have a metalbestos insulated thimble with 2" air gap on my chimney but that is through a wall not up an existing chimney.
That was what the manufacture and Stove store both recommended.
Good luck with your project