Light cannot be "accelerated" in the sense of gaining more speed. Light only has one speed, for the type of medium it is in for example a vacum or glass or anything else it can pass through.
However, for a fixed observer (which is really impossible near a black hole), the "falling" into the hole will increase the energy of the light, making each photon more energetic (each photon will see its wavelength become smaller = blue shift).
Any gravity field does that. It is even possible to measure this on Earth. The first time it was done was in the elevator shaft of a university.
A light with a very precisely known wavelength was shining straight down from the top of the elevator shaft. Detectors at the bottom measured the wavelength that was received.
The emitter was then moved to the bottom, and the detector to the top. Same thing (but shining upwards this time). Wavelengths were measured both ways and the difference matched what the calculations had predicted.
(They used gamma rays, which is a form of light with very short wavelengths -- invisible to the eye, but it is still light)
So you can't accelerate light in the way you would accelerate an object of mass, but it's wavelength can be changed with appropriate forces.
With regard to your comment about terminal velocity; Terminal velocity requires object mass, aerodynamic properties, and resistance (drag). Without resistance, terminal velocity is infinite. Use of the term terminal velocity when referring to the Universe or light is not correct.