A J-tube does not require a barrel either, just an enclosure tall
enough to contain the riser. Any RMH can be built with any shape of bell as long as part of it is tall enough to contain the core. If brick satisfies the insurance company you are good to go. Note that the International Building Code applicable to masonry
heaters specifies that there be a double wall enclosure, such as two layers of brick, so that a leak in the inner wall does not transmit through the outer wall. There are other terms some of which are slightly ambiguous like overall thickness of walls.