I think they are referring to enlarging from the muzzle itself down a few inches like we would think of the inside of a blunderbuss. In other words a 12 bore barrel would be opened up to about a 10 bore from the muzzle down for a few inches. This was common on English fowling guns and the breech area was sometimes also enlarged and "roughed". This is not a jug or tula as we know it where you go back some distance behind the muzzle and enlarge an area for the shot to expand and then be contracted again.
According to J.N. George concerning smooth bores in the early 18th century in "English Guns and Rifles"... "The fowling piece proper was, moreover, distinguished from the "fusil" by the form of it's barrel, which was not only considerably lighter than that of the ball gun, but was flared or enlarged at the muzzle, instead of being bored in true cylinder.... "
That's how I read it.
