What is the connection between the Poynting vector (EM transverse wave) and the description of photons with $E=h*f$ and $c=f*lambda$?

The Poynting vector gives the energy flux per unit of area and time. Suppose $Sigma$ is a closed surface that encloses an antenna. Then the total power radiated by the antenna is

$$P = int_{Sigma}mathbf Scdothat{mathbf n} text dSigma$$

where $mathbf S$ is the Poynting vector. Assuming that the antenna is transmitting at a frequency $nu$, each emitted photon has an energy of

$$E_nu = hnu$$

Knowing the power $P$ of the antenna and the frequency $nu$ we can estimate the photon flux $dot N$ by means of the equation

$$P = E_nudot N,$$

which is just a statement of the law of energy conservation.

More generally, if an antenna is transmitting with a spectral power density $pi(nu)$, we would have a spectral photon flux $dot n(nu)$ given by

$$dot n(nu)=frac{pi(nu)}{hnu}.$$

The total photon flux is then given by the integral over all frequencies, viz.

$$dot N = int_0^inftyfrac{pi(nu)}{hnu} text dnu.$$

Indeed, for an antenna transmitting at a pure frequency $nu^*$ we would have $pi(nu) = P^*delta(nu-nu^*)$, which yields

$$dot N = frac{P^*}{hnu^*}.$$