Is there a way of using the flow simulation tools within SolidWorks to fill an empty cylinder with a specified flow rate and as an output, get the time for the cylinder to be filled fully? This would all be done on a static cylinder in its in-stroke, all the is required is the time to find how long it takes for the cylinder in that position to fill.

I understand that I can use hand calculations to solve this (simply calculating the volume and comparing against flow rate) but I am trying to show this as a simulation also.

No, because CFD is using the mass conservation principle, which means the mass that enters the domain should exit and be the same mass. Actually should be the same mass flow rate. In your case you fill up a cavity with mass but nothing exits. I calculated the flow through a valve that lets the fluid entering/exiting a piston chamber but the calculation domain was just the top of the cylinder, the mass flow calculation was done previously on a spreadsheet. The time was set by the RPM of the crankshaft. For your problem you need multi-physiscs which Solidworks is not capable to simulate, maybe Simulia-Abaqus can.