The chimney has started going up which is some of the first above DPC brickwork so nice to see. It's thrown open a whole host of questions though, one of which is how to line the chimney (plans at the bottom). I see two main options:
Ceramic (inc Pumice) flue liner: Tubular sections that are stacked on top of a concrete (?) base plate and sealed together. You surround the sections with either granular or fibre insulation. Very much built in to the chimney and needs to be done as