Black holes aren't immune to the effects of gravity from other objects just because they're black holes. It'd be no different than trying to use a trio of stars

Black holes aren't immune to the effects of gravity from other objects just because they're black holes. It'd be no different than trying to use a trio of stars as your gravity engine (well, more space efficient). I.e. you still have to accelerate the stars, you still have to deal with slower things the stars "eat" slowing them down, if the stars pull your ship it's slowing them down. Effectively, you've just increased the mass of your spaceship by however much mass the black holes have and then still had to find something to accelerate the whole lot instead of your spaceship.