I think it's safe to assume that it's indeed human flesh.
While I don't remember any canon answer to this, it's more or less given, especially considering the latest installment, Genisys.
Pops clearly ages waiting 30 years, which is something he also mentions himself. Apart from being a sneaky way to work with the age of an actor, this also leaves no doubt to me that these are essentially human cells somehow "fed" and controlled by the endoskeleton/robot inside.
So in some way the Terminators (at least the "Arnie" series) are actually cyborgs rather than pure robots, even though it's just for time travelling purposes.
But back to the living tissue. Synthetic flesh and skin wouldn't be considered "living" by the Terminator. He clearly calls the T-1000 "liquid metal" rather than "living metal" (despite the series being able to regenerate/negate damage just like living flesh although significantly faster).
And last but not least - and possibly most important - there would be no sane reason for some intentional aging of artificial skin and flesh. Why would SkyNet implement such a thing? This won't make the whole infiltration unit more believable in any way. Throughout the movies none of the Terminators tried to infiltrate humans for significant amount of time. Besides that, actually using more skin/model variation would be a lot more effective as well. Just remember how quick they were identifying "that guy from the police station". This last point is also essentially backed by the more advanced models, T-1000, T-X, etc. all being able to use dynamic camouflage rather than relying on any fixed hull.
