We have to distinguish between a passive gravity assist and an active one using the Oberth effect.
The question you linked to is about passive gravity assists. In this situation, the math is the same for a black hole as for any other object, because it's just a matter of velocity addition. If the speeds are relativistic, then you have to use special-relativistic velocity addition. In the simplest case, where the scattering is at 180 degrees, you just need one-dimensional velocity addition. You don't need any general relativity, basically because the spacetime is asymptotically flat and the initial and final states have the spacecraft at infinity. The only difference between the case of a black hole and that of any other body is that a black hole is able to effect, e.g., a 180-degree course change for a spacecraft that is moving at highly relativistic speeds, whereas for a less compact orbit that wouldn't work.
The Oberth effect with a black hole might in principle allow extremely impressive maneuvers. Nonrelativistically, the effect comes about because work goes like $F\cdot v$, and $v$ can be very large at periapsis. Relativistically, the details will be different, but we would basically expect an analogous effect, and it could be large because $v$ can be so large.