The answer is going to be specific to the particular ammo, and require more info on what you are talking about about "flaking".
Seldom is the jacket of an actually jacketed round pure copper, but rather an alloy. For some ammo, the jacket is actually brass. Typically a brass alloy identical to the case material. For those that specify, they usually refer to this as gilding metal jackets. If the manufacturer can manufacture both cases and jackets from the base stock (usually metal ribbon where they punch planchets out of it), it reduces cost due to economies of scale (i.e. they can negotiate better prices when they buy more). These will not flake. Montana gold bullets are a good example of this. Also sometimes RMR bullets uses gilding metal.
Then you have plated lead bullets. These will look like copper because they are copper. The chemical plating process requires copper. In general these won't flake, but can under certain circumstances.
Then you have plated steel jackets. This is a soft mild steel plated with something that resembles gilding metal. S&B has skus like this. I haven't used them and have no idea if they flake. But all the examples I know of are cheaper eastern european ammo, so ZSR would be a candidate for them. They often tend to use steel cases that have been plated to look like brass.
Which brings us back to the flaking. Do you have pics? Because it is not uncommon for there to be brass dust in the fouling on a gun with any brass cased ammo. It comes from the action of feeding a round and the minor scraping that occurs on the cartridge. But it tends to look like someone took a file to brass, not flakes, with the naked eye.
I'd take a magnet to the cartridge, both projectile and case, and pick up some of the casings after use to see if the plating is scraped off.