Skeet1027,
Don't know about exact or free but the simplest definition for PSV rated flow is that flow the manufacturer guarantees and usually stamps on the PSV nameplate. As with any other equipment, the rated capacity is what the manufacturer says it is.
Now, if you want to know how that rated flow was determined, the most direct approach is to ask the manufacturer since they were the ones having rated the PSV. But, most likely what the manufacturer did was what your references in API RP-520 and RP-521 indicate...
f. The rated relieving capacity is the relieving capacity used as the basis for the application of a pressure relief device, code or regulation and is provided by the manufacturer.
Note: The capacity marked on the device is the rated capacity on steam, air, gas or water as required by the applicable code.
and
1.3.26 rated relieving capacity: That portion of the measured relieving capacity permitted by the applicable code or regulation to be used as a basis for the application of a pressure relief device.
So, if you wanted to know exactly what was involved with the rating process, what would you think you need to do?.....right, go look at the applicable code, which usually isn't free, but in some cases you can find excerpts for little or nothing....
thread1203-135368
For relief valves certified for ASME Section VIII, look at UG-131 (which references PTC-25) and Appendix 11.