Gentlemen;

What would be the right mortar for red brick chimney with a terracotta liner? Type N ?

I need to tear down the old section, to the lead flashing and redo with new brick. Below the roof line looks good.

Thank you

You'll be fine with type N. The biggest consideration for chimney life IMO is how you cap it. You want to isolate the liner from the masonry mass where it projects through the top of the chimney. You don't want the liner locked/bonded to the brick. Provide a slip of some means to allow the chimney liner to expand upward without taking the brick with it. You don't need much, just a 1/4" will do it.

Thank you!

A piece of foam around the liner and some good caulking over?

I will also be putting a stainless 4 or 5 inch flex liner in the terracotta with the appropiate weather cap after the rebuild. This is for replacing wood stove with pellet stove.

Foam, cardboard or the like. Once you have your cement cap in place and it hardens up, you can trim the foam flush with the cap and put a bead of caulking around it. I like the clear silicone but it doesn't really matter.