The Flame and the Void is a concentration technique used for focus in combat that Rand also uses for channeling. The basic idea is to think of all the emotions and distractions as going into the flame at the center of the void. Done properly, this allows the mind to fully concentrate on what's important in combat. And to make logical choices rather than emotional ones.
It is possible that some of the characters believe in a literal Void (e.g. as the eternal resting place for the Old Ones). But I believe that it is more accurate to think of it as purely a meditation technique. It makes it easier for Rand to control his channeling if he treats saidin as the Flame, but it's not necessarily true. It may simply be how he perceives it when concentrating.
There is no evidence that others who use the Flame and the Void perceive the Flame as saidin as Rand does. So there is no reason to be sure that there is a literal Void and not just a mental perception of one. You can of course prefer a more literal interpretation if you like. The books won't contradict that (although individual characters might).