Inside the event horizon of a black hole, there is no way out. There are no directions of space that point away from the singularity. Due to the Lovecraftian curvature of spacetime within the event horizon, all the trajectories that would carry you away from the black hole now point into the past.
In fact, this is the definition of the event horizon. It's the boundary separating points in space where there are trajectories that point away from the black hole from points in space where there are none.
Your magical infinitely-accelerating engine is of no use to you...because you cannot find a direction in which to point it. The singularity is all around you, in every direction you look.
And it is getting closer.note Not exactly accurate. An engine that could achieve FTL by definition can reverse time and throw you into the past, that is, away from the hole. Just point yourself in ANY fucking direction and hit accelerate: once you break the light barrier, time reverses polarity and shoots you from the hole. And a hypothetical engine that achieves FTL without time paradoxes does so by changing the curvature of space around you, again foiling the black hole. On the other hand, it's hard to predict in what exact time period of the universe will you arrive when you break free; most likely, you'll be lost in time. Oh, and, by the way, if you have a magical spaceship that just can accelerate to any velocity, you have an ability to kick physics in the nuts and take names, because screw you, Einstein. So why not just rip through the event horizon with your bare hands and march out, whistling Dixie?