what Zonie said. if you think about it, the center of gravity will be very close to the mid point of the barrel if the barrel has straight sides. if, however, there is more metal towards the back (breech) end of the barrel, this will move the C.G. to the butt of the rifle. this is a good thing because the overwhelming majority of these rifles are a good bit longer than the centerfire guys you're probably used to. ideally, the balance point of a well built flintlock will be (assuming a right handed shooter) just slightly (1/2 inch or so) to the butt side of where the shooter places his or her left hand when the rifle is brought to the shoulder. the swamped barrel helps this a great deal. it also looks longer. looks cooler, feels better and doesn't weigh quite as much (most have less metal in them- go to Dixie Gun Works or Green Mountain Barrel, or a similar web site and check out the spec sheets on a parallel sided barrel of the same caliber and length; you'll be surprised). you may also encounter something called 'profiles,' which refers to various thicknesses of swamped barrels of the same caliber. i like thinner barrels, but it's a matter of personal preference.
a relative neophyte, i'm on my third build, this time with a swamped barrel. the cost is roughly double that of a straight sided (parallel sided) barrel and, in my opinion, worth every penny. i'll only go back to p- sided bbls if the end user insists (since I am the end user, i get to say)
good luck!
MSW