You two ought to get out more.
Brass, you wont likely get to flare worth a darn, bronze, you would do better forging hot.
But for the contours, your best and easiest route is to take a good look at a tracer unit for a lathe, and see how the template can be used to provide a very reasonable way to turn an inside profile.
Not a tough job to rig up.
Even if you only rigged a pointer that could be used to follow a drawing, it would allow enough accuracy down hole, to be able to get close enough to blend the cuts together smoothly.
My suspicion, based on readings about the turners trades in England, is that the flared barrels would have been cast to size, then cleaned up by a turner working freehand with a hand held tool, similar to wood turning. That would have minimized the amount of lost material, and provided the best product with the least work.
We are spoiled for choices, when it comes to available tools and materials now.
Another cheap accurate way to machine the flare, would be to build or buy a radius attachment large enough to cut what was desired. By changing the arc center point, and the radius, a pretty fair flare could be machined repeatedly.
I suspect that this all has wandered rather far away from Brutus' original question, too.
Cheers
Trev