The method you are speaking of, sometimes called "gravity assist" is actually fairly commonly used when planning flight paths for space shuttles and probes. Using this method, space craft fly close enough to a large body of mass and use that mass's gravitational pull to accelerate, changing it's velocity and direction, in a "slingshot" manner.

NASA's Voyager 1 and Voyager 2 probes, which study the outermost regions of our solar system, used a gravitational slingshot method to accelerate themselves past Saturn and Jupiter.

Theoretically, this gravitational slingshot method should work with any object which has a large gravitational field, so it should work with a black hole too. However, there are certain considerations to take into account. If anything gets too close to a black hole, no matter how fast it is going, it will get pulled in and can never escape, therefore a space probe would have to stay much further away from a black hole than a planet. Beyond that though, there is the issue of distance. All known black holes are VERY VERY far from Earth. The closest black hole is about 2800 light years away from Earth, that is about 16,000,000,000,000,000 miles. Just to refresh your memory, a light year is the distance that light can travel in one year. Compared to that distance, Voyager 1 is the furthest human made object from Earth, it is only 12,000,000,000 miles from Earth. That means the closest black hole to Earth is over 1 million times farther away than any human made object has ever traveled, even considering that it has been traveling for over 40 years.

So, long story short, I would say that it is theoretically possible to accomplish such a maneuver, it is highly unlikely that humans or any human made object will ever travel close enough to a black hole to actually try it out.

I hope this answers your question!