Todd;
This is another one of those situations where a pro should be consulted.
You might be OK going through a stone wall to get outside, but....
Have you ever seen what happens to an uninsulated pipe when you vent gnarly thick greasy smoke thru it? The smoke cools, the crud condenses out and either plugs the chimney [lucky] or the gunk ignites and you simulate a shuttle launch on the side of your building with whatever thin pipe you have containing a LOT of heat. If its regular steel it will glow red then it will collapse with all the joy that brings to the vicinity.
Be very careful with venting this stuff. Consult a qualified installer for information. I used to install chimneys as a side business and have seen the results of "on the cheap" plain pipe chimneys up the side of a building. Its not a pretty sight.
Personally, if I had to burn something like this I would use a gasifier to extract the volatiles like making charcoal somewhat. This would require more effort and a vessel to "cook" off the volatiles and then burn the gases. Not real sure of this material you have tho. If it burns you can probably gasify it.
Try this experiment:
put a gob of this goop in the bottom of a paint can. poke 6, 8 or 10 holes around the upper sides above the liquid level of the goop with a nail. pop the lid on. Build a small fire. Set the can in the fire. After awhile the goop should start boiling off and the holes let gases out which will ignite and burn very much like propane or natural gas. Sometime sooty like acetylene but probably cleaner than the direct burning goop.
Anyway, I digress.
Beware of doing what you propose with the chimney. The barrel will probably be ok awhile but hot fires oxidize them away pretty fast.
More than one way to defur a feline of course.
Cheers.
TomW