There's very simple approach when you think of relief valve design.
(1) You should not consider any "favourable" response from the control systems. It means that the all the streams coming in and out of your system should be considered as operating at its normal position. If I further explain, you should not consider any increase or decrease in flow rate from system except the one which is causing "overpressure".
(2) After considering above aspect, take a stream which is causing overpressure due to higher flow than normal. In your case, it's gas break through from a high pressure system upstream of a stripper. I presume that you already know and calculated what is the possible flow if there is gas break through from control valve full opening.
Based on both above (1) &(2), Let's say the gas break through flow = "x" kg/hr.
This is maximum vapour flow possible from control valve full opening considering selected Cv. Remember, if there is by-pass to this control valve, you need to consider that by-pass valve is also fully open for finding out total possible gas break through. You can refer API-521 for all these guidelines and recommendations.
Hence, PSV needs to be capable of the "x kg/hr" calculated as above to relieve it to flare header. Then only pressure in system will remain below design condition. Hence, the flow into system and out of system are equal which is "x kg/hr". This is the basis PSV sizing.
Practically, instrumentation system may respond favourably before PSV starts releasing to flare system. Hence, actual flow might be lower than the value specified as "required relief". But it does not have any significance as far as safety of system or sizing or relief valve is concerned.
I hope this helps.
Warm regards,