The following is quoted from George Shumway's book Recreating the American Longrifle copyrighted in 1970.
Tapered-and-flared barrels or swamped barrels are largest at the breech, and taper to a minimum diameter 6 to 10 inches from the muzzle, than flare out somewhat to the muzzle. Barrels of this type not only balance the best in a rifle but they also look the best. German flintlock rifles of the 18th century almost always had barrels of this type. The flare or the enlargement at the muzzle is aesthetically pleasing, it provides a higher base for the front sight than a straight tapered barrel would provide and it adds a little mass at the end of the barrel, which is an aid in shooting.
Another advantage of the tapered-and-flared barrel is that it provides for a subtle slendering of the stock from the breech to muzzle which adds to the beauty of the rifle. It also aids in making a waist region that is architecturally pleasing. It is a fact that almost all of the old rifles of the flintlock period had swamped barrels though on many of the late ones it was a minor feature.
:-)