What vertical separation is required in a holding stack to avoid wake turbulence?
The minimum vertical separation in a holding stack is no different from the minimal vertical separation used elsewhere. This is almost universally 1000 feet. In countries where Reduced Vertical Separation Minima (RVSM) has not been implemented, 2000 feet of vertical separation is required above FL290. 2000 feet is also needed if a non-RVSM equipped aircraft (such as certain older military planes) is flying above FL290. However, not many holding stacks grow to above FL290.

A point to consider is the fact that aircraft produce the most wake turbulence when they are flying slowly for landing. So since 1000 feet is enough during approach, it should also be plenty in a holding stack.

There has been some evidence that 1000 feet of vertical separation may not be enough for certain, heavy aircraft types. In 2017, a Challenger jet had an accident after passing 1000 feet below an Airbus A380 during cruise, presumably because the smaller business jet hit the wake turbulence from the A380. See AVHerald for details. However, this has not (yet) resulted in changed separation minima.

1000 feet is not enough to prevent planes from "flying in each other's wake turbulence" as you say, but in most cases it should be enough to ensure that the wake turbulence has weakened enough to not pose any threat to the lower aircraft. Also remember that wind can have a significant effect on the spread and dissipation of wake turbulence, so on days with a certain wind direction and velocity, the wake turbulence may survive longer than other days.

But the answer to your question remains the same: the vertical separation to be applied in a holding stack (below FL290 and during RVSM) is 1000 feet.