What type of dry gas seal (DGS) are you considering (single, double, tandem)? This would be my first immediate question.
Say for a typical tandem, if you are using N2 for separation seal (or barrier seal) and for intermediate labyrinth (secondary seal), then the total N2 flow rate to the DGS cartridge is the sum of both separation and secondary flows. In particular for the barrier seal, the N2 flow rate will change considerably depending on the type of separation seal : labyrinth or carbon type. In general the labyrinth type barrier seal is a robust solution but has the highest leakage rates. Basically figures differ from one supplier to another and I don't think it is something you can calculate. You may have some standard tables or a program readily available from DGS suppliers that may help. If the separation seal is a labyrinth type and is provided/manufactured by the compressor manufacturer, they should have some internal program to calculate the rates. If the separation seal (both labyrinth and carbon types) are provided by the DGS manufacturer - which is usually the case - then you should inquiry the leakage rates to them as well as for the secondary seal.
Consider that it may also happen that the N2 can be used for primary seal and again you would have to go and ask DGS suppliers for leakage rates figures. The complete picture of N2 flow rate will depend mainly from the seal operating conditions, shaft end details and flare back pressure for a given seal gas manufacturer.

This is something you can't "calculate", but simply need to identify your seal make, model and size and then look it up in the vendors website and add up all the seal leakage rates. That's about all the "calculation" you can do.

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

Sabergg1981
As a guide for buffer gas the seal needs to have an intermediate labyrinth and use a velocity of 3 m/sec. For the separation seals or barrier seals if you have a labyrinth use 12 m/sec. Make sure that you filter the gas supply at all times.

Trust this helps and if you have the labyrinth details you can calculate the flows.