That wouldn't get anything up to relativistic speeds. The universal rule of slingshot manoeuvres is that you depart from the slingshotting body at the same speed you approached it, just in a different direction (in the slingshotting body's frame of reference). Therefore, the maximum velocity gain you can achieve with a slingshot is governed by the velocity of the slingshotting body - the black hole. Which, as far out in the extremities of the solar system that it is, is not very fast.
If the black hole is rotating isn't the reference frame in motion about the center of the black hole in addition to the orbital velocity about the sun? i.e. frame dragging?
You mean https://en.wikipedia.org/wiki/Penrose_process - it doesn't look like it is very efficient or effective, and you'd have to get so close to the black hole that you'd be shredded to get anything at all.
