I guess that I am in the minority on this one but I feel that flutes do add at least some stiffening properties to a barrel as well as making a large diameter barrel lighter. The more surface area a barrel has the harder it should be to bend or flex it.

However some barrels can not be fluted. I forget which ones they are but I believe a hammer forged and one or two others can not be fluted with out weakening the barrel and adding more stress to the steel.