There is no point in using stainless, let alone triple wall, around the riser to hold insulation. Simple black stovepipe will work fine for little cost.
I would advise using rigid insulation that will hold its shape when the steel riser burns out. Steel in a burn tunnel and riser will corrode quickly when the fire heats it to cherry red for hours per day. If you do not insulate, the steel will last longer because it will radiate away the heat, making the combustion much less efficient and much dirtier.
A good rigid insulation for this purpose would be a mix of mostly perlite with just
enough fine clay to make it hold together. Fireclay, available from masonry suppliers in sacks of powder, is the best for this purpose.