Insulate or not>

6" pipe run the full length of the chimney, all 23' of it. If you cant insulate, that would be better than just a 6' section. An insulated pipe should provide better draft on an exterior chimney. not as much on an interior. But a full length liner will provide better draft than your 6' section. Its also safer and easier to clean. I have a 23' interior chimney, 6" pipe, no insulation which runs great.

How are your flue tiles? If cracked or bad shape code requires insulated liner, if they are ok I'd just stuff the top couple feet with ceramic wool insulation.

No doubt your best choice would be 6 inch liner from stove to chimney top. Then insulate with a poured in vermiculite. You will be much more likely to have a well functioning Oslo if you do this.

Chances are if you do not line the entire chimney your draft will suffer.

The issues at play are first, code compliance/safety, then performance.

I would suggest removing the clay tiles and installing the needed 6 inch liner with insulation wrap.

Follow the instructions for the liner when you insulate - some liners don't include instructions for insulation, and wont meet the ULC specs if you do insulate them as they would be installed contrary to instructions. A circular loop I know, but one to pay attention to if you or you insurance company is going to be concerned about meeting code requirements. The point here is only by a liner that has specific instructions concerning insulation, and follow them.

Read the liner related links in my signature block for more info if you wish.

I would recommend the 6 liner with insulation. Insulation is key to how much smoke/draft will be let in and out. I know there are some kits out there that may be helpful.

I had a 6"X10" masonry with tile liner of about the same height, and of course an insulated 6" SS will not fit, so I installed it uninsulated and did what some others have suggested, sealed the lower and upper ends with insulation. It provided a good draft with a minimial amout of work.