I understand that you want to calculate PSV discharge pressure at outlet flange.
Whether the psv relieving to atmosphere or to flare header, following general guidelines are common for calculating PSV discharge pressure :
1. There will be 2 contributors for this discharge pressure: superimposed backpressure & built up back pressure. one is due to geometric configuration of downstream network and another is due to effect of actual flow through given path.
2. you need isometric drawings, PSV sizing data, PSV discharge flow & properties, flaresim software, possible relieving scenarios to calculate same.
3. Build model in flaresim and insert actual data. you will get actual pressure at PSV discharge.
4. If you use flaresim, you can get corresponding mach no. as well. This mach no. is useful to piping engineer to identify stress critical lines and further do support calculations for same.
If approximate data required then consider flare tip pressure drop ....plus.... calculate possible pressure drop across piping by line hydraulics check. you may consider this value with some margin of safety.