The "dynamical friction of photons" is a particular case of "dynamical friction" and it is particular only in this that it is related to photons. Everything else is the same as in ordinary "dynamical friction".

A model of such a phenomenon might be an object moving through a stationary (e.g. virialized) cloud of dust not colliding with the dust particles of the cloud. The object by its passage though the cloud agitates somehow the cloud through gravitational interaction so the cloud particles gain kinetic energy. The total energy of the cloud and the object that moves through it remains constant and so the kinetic energy of the object becomes smaller. This reason for the loss of kinetic energy of the object due to its passage through a cloud of dust without touching the dust is called "dynamical friction".

Now, if the object is a photon, it can lose energy too. However for the photon the loss of energy translates into its redshift, and so a passage of a photon through a cloud of dust is bound to result in some kind of redshift.

It all happens in a stationary space. Therefore we have here a qualitative reason for a Hubble type redshift in a stationary space. Now we need to investigate it quantatively.

We can't use for the calculations directly the Newtonian gravitation since Newtonian gravitation doesn't work for photons. So we are using the following trick: we take a space with a uniform distribution of dust and radiate out photons from a certain place in that space. The space becomes less uniform, which means gravitational field gets created, and when the photons are gone we can use our Newtonian gravitation again to calculate gravitational energy in this field. We know that it has to be equal the energy lost by the readiated out photons. Then we may convert it into thie redshift (Z) for specified density of space (rho) and the distance traveled by the light (x).

To make long story short, this method of calculating, gives us redshift
Z=x*sqrt(4pi G rho)/c ........ (1), where (G) is Newtonian gravitational constant and (c) is speed of light.

If we take redshift (Z) for Doppler redshift resulting from expansion of space we may set the Hubble constant for this expansion as
H_o=Zc/x=sqrt(4pi G rho) ........ (2)

For density of space 6x10^{-27}kg/m^3 we would have H_o=70km/s/Mpc which is observed in our, supposedly expanding universe.

It is interesting, that when we put into (2) the value of the radius of curvature of Einstein's universe (R) then our Hubble constant simplifies to
H_o=c/R ........ (3)
suggesting that the only reason for the Hubble redshift in the universe might be its curvature of space.