As others have said, be aware of what you have!!!
If that was a chimney for an earlier burner, wood or coal, you should be fine if it's in good shape. Since you say clay tiles, I ASSUME it was a fire type chimney, I could be wrong though, but I don't see clay tiles used for much else.
As for the actaull question you asked,
"where and how should I reduce it from 8" to 6" to have the best chance of not filling the room with smoke"
It does not really matter. What matters is the chimney works well for this, and does not leak fumes into the house. From 8" to 6" itself if I could I would do right at the wood burner with a new flue ring. If your going from 8" round pipe to 6" square then as said by another, a few hammer hits and your done. Just make sure it don't have leaks.
As for filling the room with smoke, that depends on many things, not just flue size.
Straight up and out is the best. Start adding bends and twists and you restrict flow.
6" straight up works best for me really, but I have a flat roof right there and up and out leaks bad!! I can't stop the leak with the pipe installed. So I went back to 90 over out and 90 up. It does not work as well for flow but stops the roof leaks.
Draft is maybe your main thing, and is effected by many other things. The more bends the less draft. The less heat in exhaust the less draft. Now if you have a very well sealed house also less draft.
Something many people don't think about is other drafts!
Ok here I have a fireplace with a large flue, I have a woodburner. Guess what happens if I used both at once and do not open a window wide!!! YA, the fireplace draft will suck up the smoke from the fireplace great, BUT it also sucks smoke out the woodburner with a negative draft there. OR with a low fire in fireplace and big fire in woodburner I can suck the fumes and smoke out of the fireplace into the room.
I can use either one anytime, or both if I open a large window wide!
For a feastive fun thing once I did open a window wide in middle of winter and use both at once. But lack of interest in FUN stuff of family here we never use the fireplace for anything. I might as well rip it out and have that much more wall and floor space