Photons can be counted, so you'd think that the number of photons in your flashlight is an integer, and that a graph of the number of photons in your flashlight must go up in jumps.
However, quantum mechanics is not quite that simple.
While photons can be counted, you are not guaranteed to have an integer number of them unless you actually do count them. (Formally, you have an integer number when the field is in an eigenstate of the counting operator. I'm not quite sure exactly how the counting operator works, actually, but every quantum measurement must be associated with an operator by the formalism ).
If you don't count them, then it's perfectly possible for there to be a non-integer number of photons in your flashlight (on the average, this is called an expectation value). This is because the electromagnetic fields in your flashlight could be in a a "quantum superposition" of states. This is one of those weird quantum phenomenom that really don't have any good classical analogue.
Given this possibility, though, there's no need for the graph of photon number vs time to go up in jumps.
The fact that photons don't have a number unless you count them is similar to the way they don't have a position unless you measure it, and they don't have a momentum unless you measure that. And when you measure the position, you affect the momentum, and vica-versa.
On a practical level, one photon more or less isn't going to be measuarble anyway. So you're better off thinking of your flashlight classically, unless you design your flashlight so that it only emits a few photons.
