I've finished the kiln chamber, all that's left is to trim wall bricks to the arch and cover it with a couple layers of fiber. Then on to the chimney.
Here is a detail of how the wall ineracts with the arch. The walls are two bricks deep(9") and are half under/half outside the arch. This helps structurally to stabalize the arch as well creating a strong semi-airtight joint where the arch meets the wall(similar to a lap joint in woodworking).
The laborious task with catenary arches is the amount of brick cutting that is needed. But there is indeed nothing prettier than a catenary arch kiln, for me anyways.