Fluting will increase barrel stiffness. A crude example would be I-beams in large buildings. If you took the same material and made a solid bar it will not be as stiff as the I-beam.
I must admit, I used to believe this to be true. I cannot provide the necessary links to prove it, but have seen enough to believe this is wrong.
Several people have hit on the right answer.
Nutshell version:
A fluted barrel is a compromise between stiffness/accuracy, and light weight.
An unfluted barrel of the same diameter as a fluted barrel will be a little stiffer, and theoretically more accurate
A fluted barrel of the same diameter as an unfluted barrel will be a little lighter, but slightly less stiff.
A fluted of the same weight will be stiffer and more accurate than an unfluted barrel which has to be thinner to weigh the same.
I don't think it will make a bit of difference in longevity. If you want the stiffest, most accurate barrel buy a standard, or heavyweight non-fluted barrel. If you want a trim lightweight rifle buy something with a pencil thin barrel similar to the Remington Mt Rifle. If you are looking for a compromise, buy a gun with a standard weight, but fluted barrel.