Although I had little idea what I was about when it came to building the chimney, it turned out to be fairly straightforward. Design-wise, the outermost opening should be slightly larger than the oven door, and the chimney itself should have a fair bit of height, otherwise it won't draw the smoke out properly.
I didn't take many photos of this stage, but what's here gives enough of an idea. The brick work is a little crude, but the overall effect is quite pleasant, I reckon, especially the arched opening, which I describe below.
Getting the chimney to fit around the dome required a bit of fiddling about - having an angle grinder fitted with a diamond blade will save you a lot of trouble here.
For the arched opening, I fashioned a temporary frame out of timber offcuts and a length of steel I bashed into an arc shape with a club hammer. I slightly tapered the bricks in the arch (cutting them with an angle grinder fitted with a diamond blade). Once all the bricks in the arch were in place, I removed the frame (carefully!) and voilá - there you have a self supporting arch!
I was very curious to see if the chimney would work as intended, and was delighted that it did! When the wind is up the smoke swirls around a bit, until the oven gets cranking, then the intense heat drives the gas and smoke up and out.
In an ideal world I might run the chimney into some kind of flu system, which would draw the smoke out even better. But for an outdoor oven, what I've got here works just fine.