Matt Alemeda--yes, the flutes increase the strength of the chamber. Don't recall whether I learned this in a Mechanical Engineering or a Metallurgy class, but at the time I believe Ike still shot a decent round of golf.
My metallurgy professor, back in those civilized days, came in to class with an M1 rifle. Stripped it down, we had to decide what metal we would use for each part, how (or whether) we would heat treat it, and how would we make the piece in the first place. That is, forge, cast, stamp, machine from bar, cold draw, &c.
When the piece fires, the chamber is under uniform high gas pressure all the way around. When metal is stressed, it stretches, just like a spring. Removing some metal between chambers makes the expansion (stretch) more uniform, rather than concentrating that strain (stress, if you prefer) on the outside diameter of the cylinder, right over a chamber.
If it were practical to do so, the strongest revolver cylinder would be six smooth tubes, perhaps glued together. Kinda hard to rotate & lock such a device, so fluted cylinders are the best bet.
The earliest fluted cylinders I personally know about were Sam Colt's fluted cylinder 1860 Army. Dunno why he did it. Unfortunately,these cylinders were fluted too far back & burst simply from being too thin at the rear. He replaced these first, mostly burst, cylinders with more fluted cylinders, however the new ones had a tapered chamber so the rear portion near the nipple was thicker.
When any gun fires it is important that the barrel expand as uniformly as possible, to avoid concentrating stresses. Generally speaking, modern firearms are designed to do so.
A cool example of what happens when you restrain uniform expansion is to clamp a modern barrel (without the stock) in a good, strong machinists vice. Load, then pull the trigger. Using a long cord. The barrel cannot expand sideways, because the mass of that large vice restrains it. So all expansion is on the top and the bottom. The barrel will split.
I personally don't personally know if this will always split a centerfire rifle. But in Ancient Times (1940's, 1950's) it was widely known to.
I am not going to argue stress analysis with anyone. If you would like to know more about this, consult a mechanical engineer, preferably one with gray hair.