Photons "rate of fire" I'm not sure if this makes any sense but, do photons "discharge" from a source at an infinite rate?
 A: You are asking about the number of photons fired from a device such as a laser at a unit time. We cannot say what the precise number of photons would be at any interval due to a version of the Heisenberg uncertainty principle:
$$\Delta E \Delta t \geq \frac{\hbar}{2}$$
It basically states we cannot suppress our uncertainty about energy fluctuations in time, such as in a light source, under a certain limit.
However, for any device we can say with certainty it will not fire an infinite number of photons in any time interval. Why? Because the probability of any distribution of "fire-per-time" can be non-zero for any number, but the total probability of all events has to be normalized, i.e.
$$\sum_{i=1}^\infty P( i\; {\rm photons\; in\; given\;time \; interval }) = 1$$
The convergence of the sum has a necessary condition that
$$P(\infty {\rm \; photons \; fired}) = {\rm lim}_{i\to \infty} P( i\; {\rm photons\; in\; given\;time \; interval }) = 0 $$
That is, we are certain any device will not fire an infinite number of photons at any given time interval. Any photon rate of a physical source of light will thus be finite. 

This is a formal analysis and could be in principle circumvented. But think about it in a different way. Say every photon is carrying a fixed finite energy. Then an infinite number of photons per unit time would mean an infinite amount of energy per unit time. This is obviously not a property of any possible physical device.
