What is the proper way to sleeve and extend?

[RobMoyer]

In the process of researching the installation of a lopi revere into a heatilator mark 123.
Had the fireplace inspected and it checked out great. The insert is rated for the installation
and I am thinking of using a combination of Stainless steel Tubinox and SS Flex to line the current
setup. I also need to extend my flue up a couple feet, because it is about even with the roof height
less than 10 feet away. I plan on raising it 4 foot.

I have read the outside wall of the existing chimney is used to draft down cold air to cool the outside
of the fireplace and when sleeving the 6inch you shouldnt block off that area with a simple reducer.

I am a bit confused on this, so can someone point me in the right direction for the
best way to extend and also sleeve with 6 inch? If you can point me to the correct parts that
would be a bonus. Any pictures would be awsome. I will throw a picture of the ugly ass chimney.
I am residing it and having a new cap fabricated, and yes that is OD 14 inches standard for the mark 123s.
The old owners complained it would never draft right, and it showed when we painted the ceiling lol.

I allready have the revere. I bought it from someone who bought it but was unable to install it due to
a divorce and subsequent house loss.

 

[RobMoyer]

Shameless bump

 

[RedGuy]

I think it basically comes down to what ever will work for your application. I'm choosing to add an additional flue tile to my chimney with the liner inside. It'll probably look pretty dumb til I can rebrick it next spring, but it'll be functional.