In order to match staged turbos, you normally start with the 2nd stage first, then calculate what is required from the first stage to supply the second stage. You need to account for the pressure change and temperature change from compression and intercooler effectiveness plus pressure drop- in other words density ratio. Flow on compressors is described as INLET flow, prior to compression. Lots of people miss this very important point. You need to know the pressure ratio, compressor efficiency, intercooler effectiveness and intercooler pressure drop in order to calculate density ratio which is really what's important.
Normally, you try to keep the pressure ratios between stages about the same.
In a simplified example, assuming no temperature changes, no pressure drop and a pressure ratio of 2 between first and 2nd stages, you'd need about twice the first stage inlet mass flow (before compression) to feed the 2nd stage at that required inlet flow (now at double the pressure).
When both compressors are about the same size as in Raptor, the 1st stage will certainly be in the choke region trying to supply the 2nd stage compressor. Operation near choke results in low compressor efficiency and high compressor discharge temps- exactly what you don't want where you're demanding the already high pressure ratios that diesels require to make any sort of power at high altitude.
Calcs can be done using volume (CFM in old terms) or Mass (lbs./min. usually in old terms). I use mass since that's how modern Garrett compressor maps are labeled.
An easy to visualize example of the physics here, is to look at a cutaway of an axial flow gas turbine engine. The first compressor stages are larger than the downstream stages and on the turbines, the first stages are smaller than the downstream stages. The same physics applies to staged turbochargers.
