Chimney material?

After making my core out of fire brick with a 6.5 inch hole can I use cement blocks as the exhaust? Or would they have too small a hole?

You never want the cross section of the exhaust to go below the riser dimensions. If you are building a 6.5" diameter heat riser, you want to maintain 6.5" inches throughout. Use material that is rated for high temperatures, cement will fail at relatively low temps.  http://donkey32.proboards.com/

Your exhaust,post mass,shouldnt be very hot at all.
Cheap stove pipe should be plenty good enough.
About $5.00 for 2 feet at Menards, 4 feet for $22.00

You would have to measure the specific blocks available to you, to see if they have at least the same area as your riser. If so, they may work fine as the channel for your mass. As mentioned, the heat levels in the mass are not likely to be high enough to damage the blocks. Be aware that rough inner surfaces, or the steps you get from the slight difference in dimensions from one side of a block to the other, will increase turbulence and friction.

I might use both cores of a block as parallel flue paths, depending on how much space you have. As long as the paths end up being essentially identical, you would probably get reasonably equal flow through them; minor differences would not matter that much in this application, especially if you let the channels recombine at each turn.

I agree with William Bronson , use stovepipe, the whole stove can with great advantage , especially if inexperienced at masonry work, be built around a 7 inch stainless( preferred) stove pipe including the right angle or after. this makes it  much easier to build around with firebrick and or common solid brick which will take much more heat than concrete block. It will be much faster to lay up the brick around the pipe. Just secure the pipe well at top and bottom. the steel will also draw better than a narrow block or brick channel.  
Also a 7 inch flue gives a much better draft than 6 . We always use 7inch liners for fireplace flues, and of course the firebox can be 12-16 cubic feet in size, firebrick lined.

Daniel Ray wrote:You never want the cross section of the exhaust to go below the riser dimensions. If you are building a 6.5" diameter heat riser, you want to maintain 6.5" inches throughout. Use material that is rated for high temperatures, cement will fail at relatively low temps.  http://donkey32.proboards.com/

So how much room do I need to leave between the drum and top & sides of the riser/insulation?
I was planning 1.5 inches of slip and perlite for insulation around the riser.

2" is a good minimum top gap between riser and barrel; for a 6.5" system, 1 1/2" may be enough, but 2" is safe.

Side gap would preferably be at least 1 1/2". If the riser is not centered in the barrel, the side with more space is likely to get hotter due to more airflow.

Did you build the riser with firebrick laid flat or on edge? Full or split (half thickness) brick? The less mass in the riser, the quicker it will come up to full operating temperature. Around a firebrick core, I think 1 1/2" of perlite-clay should be okay. More is better if you have the space for it.

Glenn Herbert wrote:2" is a good minimum top gap between riser and barrel; for a 6.5" system, 1 1/2" may be enough, but 2" is safe.

Side gap would preferably be at least 1 1/2". If the riser is not centered in the barrel, the side with more space is likely to get hotter due to more airflow.

Did you build the riser with firebrick laid flat or on edge? Full or split (half thickness) brick? The less mass in the riser, the quicker it will come up to full operating temperature. Around a firebrick core, I think 1 1/2" of perlite-clay should be okay. More is better if you have the space for it.

It was built on edge with split fire brick
Any tips on the chimney then if I can't use cement? I'm still planning to use 12"x12" cement step stones around the insulation of the core to protect it. I'm hoping the perlite will protect it from the heat.