This is from Precision Rifle Blog.com. It is rather lengthy but it good info.
"There are some people in the shooting community that do believe fluting affects a barrel’s accuracy in a negative way. In fact, Shilen Barrels refuses to flute their barrels. Here is what they say on the topic:
Fluting is a service we neither offer nor recommend. If you have a Shilen barrel fluted, the warranty is void. Fluting a barrel can induce unrecoverable stresses that will encourage warping when heated and can also swell the bore dimensions, causing loose spots in the bore. A solid (un-fluted) barrel is more rigid than a fluted barrel of equal diameter. A fluted barrel is more rigid than a solid barrel of equal weight. All rifle barrels flex when fired. Accuracy requires that they simply flex the same and return the same each time they are fired, hence the requirement for a pillar bedded action and free floating barrel. The unrecoverable stresses that fluting can induce will cause the barrel to flex differently or not return from the flexing without cooling down a major amount. This is usually longer than a shooter has to wait for the next shot. The claim of the flutes helping to wick heat away faster is true, but the benefit of the flutes is not recognizable in this regard until the barrel is already too hot.
Several months ago, I asked Shilen for any data they have to support these claims, but they never responded. So this smells like it could just be a strong opinion and theory, and may not be backed by any empirical data they’ve gathered.
But an article written by Tom Beckstrand in the 2013 edition of SNIPER magazine summarizes some tests that Accuracy International performed to determine whether fluting a barrel affected accuracy. Here is an excerpt from that article:
One design change that resulted from AI’s exhaustive accuracy testing and development of the PSR [Precision Sniper Rifle] is the removal of flutes from the barrels. Engineers at AI decided to isolate the barrel flutes to see what impact they had on accuracy. The engineers attached a laser to the rifle’s receiver, another to the barrel, and a third to the scope. All three dots were zeroed at the same point, then they started shooting the rifle. They discovered that, no matter which fluted barrel they used, the dots would diverge as the barrel heated. The dots from the devices mounted to the scope and the receiver would stay in place, but the barrel’s device would manifest a point-of-impact (POI) shift. The POI shift from the warming barrel greatly diminished when they used barrels without flutes.
Engineers determined that the flutes never heated evenly, causing the POI shift. I hope the results of this test gain wide circulation through the sniper and long-range shooting communities to help eliminate some of the ignorance that surrounds the perceived advantages of barrel flutes. Flutes are great for shaving weight, but this is the first test I’ve heard that provided empirical data detailing what happens when the barrel is fluted. This should be the death of the “they cool a barrel faster, so they’re more accurate†argument, listed among flutes’ virtues. Our goal is and should always be to mitigate the effects of heat; fluting exacerbates it."