Others can provide a more complete analysis procedure for each individual case. But a pump coupled to a VS drive will have flow proportional to rpm only if the required developed head varies by the square of the rpm; if the required developed head is a constant value, then there is no value in the VS drive, as the available developed head will be less than required for all rpm < 100% design rpm.
In the worst, case, the pump is pumping liquid up to a tank at a fixed, higher elevation, such that the required developed head is nearly cosntant irrespective of flow. In such a case, a constant speed pump serves well.
In the best case, the pump is feeding a piping system which has a developed head which is exactly proportional to the square of the flowrate, and all developed head is related to frictional loss in the piping system. In that case, a VS drive makes sense.
Of course, the economics of what sort of VS drive to use is another matter- VFB seems to be most economical below about 200 HP, while hydraulic VS couplings become competitive above 200 HP.