the massive particle that is sent at the black hole at speed 0.999 c
will follow approximately the same trajectory as the photon
if you want to make the approximation better, send a new particle at
and then one at 0.99999 c
the particles follow geodesics in spacetime---the spacetime created by the massive central body, the black hole. approximately the same paths as photons of light
if you think about it in an open-minded fashion, I believe you will come to the conclusion that the maximum radial velocity (what you asked about in your question) is c.