Has the velocity of photons coming from black holes already been measured? Has the velocity of photons, which are coming from black holes, already been measured? I am not aware of such measurements.

The reason for the question is the following: If space-time near black holes has some extra dimensions, than photons created in this higher dimensional space-time might have non-zero components of the wave-vector in these extra dimensions. On the earth however we see just our 3 or 4 components of the wave-vector, so we might see just the projection of the original wave-vector onto our (3,1)-dimensional space-time. In this case the velocity of the photons might be less than the standard velocity of light.

I have in mind a special model of our universe. I believe, that our universe is the horizon of a (4,2)-dimensional space-time. On this horizon (which is our universe) we do not see the extra dimensions, however, they should be visible near black holes. So, in this model, black holes are the windows into the extra dimensions.
No.


Photons can't come from the singularity of a black hole, or from beyond the event horizon.
While some very good candidates for black holes exist, none have been certainly observed.
We have never observed Hawking radiation: it remains theoretical.
We have observed radiation from the accretion disk of likely black holes, however the matter in this disc is orbiting in 'normal' spacetime.
Direct measurement of the speed of individual photons is pretty much out of the question. We can measure the speed of light by creating photons at one point and then timing when those photons arrive at another. You can't measure a photon's passing, as to measure it you would have to interact with it. If you interact with it, it is no longer the same photon. This leads to...
When we speak of a photon travelling from one point to another, remember that it is a quantum process: the photon interacts with matter and with itself. Photons are not classical particles. Everything about them needs to be considered through quantum electrodynamics.
The flashes from pulsars are coming from a region of intense gravity. They do propagate at the speed of light: pulsars measured from different locations flash at slightly different times due to light travel time. There is nothing special about the space-time outside of a black hole as compared to that around a neutron-star, only a difference of degree. Gravity is still pretty intense around a neutron star, $g\approx10^{12}\mathrm{ms^-2}$
Gravitational redshift from white dwarfs is well known. Gravitational redshift is predicted by relativity, which assumes a constant speed of light. 
Constant speed of light is pretty fundamental to relativity. If a theory breaks this, a lot of other physics is broken (exceptional claims require exceptional evidence)