Hi,
They were filed or ground into the tapered and flared shape. German, French, and British barrel makers used large grinding wheels powered by water. Remember, in Europe and Britain, specialists made different components and barrel makers worked full time just making gun barrels. In America, individual shops might make a few barrels but most were imported from England or Germany. Also barrels were made from wrought iron not mild steel like today's barrels so they were easier to grind and file. I believe there is an example of a French barrel grinding table or bed shown in Diderot's "Encyclopedia" , which could control the taper and flare dimensions. The Spanish, who only made smooth bored barrels that were mostly octagon to round, hammered the flats and taper into the round tube for the octagon section, and then turned the round portion on a lathe, cutting the metal away with former's chisels. They used gauges or templates to make sure of the dimensions at different locations along the barrels. They were so skilled that the octagon sections were virtually finished even and smooth with the hammering. Only a little filing cleanup was needed. The gauges used to check barrel dimensions are the origin of the old term for octagon barrels as "square" barrels because the gauge was a square notch not an octagon. It did not need to be octagon because the square shape, easier to make accurately, checked 4 of the flats and then rotated 45 degrees, checked the other 4.
dave