Slingshots work by gravity interaction between a massive body in motion and a second body in motion. Any massive object can be used.
The problems with a black hole are (1) avoiding the capture range, (2) surviving the radiation, (3) surviving the accretion disk contents, (4) the extreme distances involved.
Keep in mind: black holes can have tremendous distances with gravitational effects. Distances which can be measured in light years in some cases, and thousands of AU even for smaller ones.
The strength of the boost is a factor of how close one gets, and the correct angle of insertion relative to the motion.
The further out, the less the acceleration/deceleration. But also, the further out, the less the radiation from the accretion disc collisions, the less dense the accretion disk, and the less Hawking Radiation.
The immense distances also require immense amounts of time.