Let us accept (for shits and giggles) the idea of a "gravitational slingshot."
Let us accept the idea, according to the images provided by user 4pir2, that Pluto was just outside of perigee (or perihelion) for New Horizons, and had Pluto been present, Voyager 1 would have been encountering Pluto at a closer distance.
So, for Voyager, with the travel time to exit listed at 12 years to travel roughly 2.7 billion miles, that equals roughly 26,000 miles per hour, with the "slingshots."
New Horizons, lets just estimate at 2.9 billion miles travel distance. Time at 9.5 years = 35,000 mph, with no slingshot.
What kind of engine can impart more velocity to the object it is propelling than it is generating in terms of thrust?