A lot of people might not agree with this but when it comes to questions about barrels it's usually best to ask the people that make them. Here's a quote from the Shilen barrel website.
Welcome to Shilen Rifles, Inc.
What about "fluting" a barrel?
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.
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