Many of the salient points have been touched, but there is a sentiment amongst many benchrest and F-class shooters that fluting leaves a barrel more vulnerable to shfting POI as it heats up if the fluting is not done with precise and uniform depth and spacing. However The same thing can happen with barrels with steel of poor homoginicity.
The depth of fluting is not that great, so I would argue that its cooling benefits are negligible (Because the throat is the most impacted by barrel heat anyway). The only tangible benefit is a small reduction in weight.
Fluting is going to make future attempts at setting back and re-crowning to look weird. I personally feel that the only true benefit is cosmetics...whatever floats your boat.