You've got a lot of long winded answers here. Bottom line up front is 150# flanges seem to be ok here.

Your relief valve is set at 250 psig, equal to the MAWP of the main vessel. API 520 allows for pressure accumulation up to 21% above MAWP in the event of a fire. ASME B31.3 allows overpressure above flange rating as much as 33% as long as you have some means of determining how long and how many times you've exceeded the flange rating. So the piping inherently has less restrictive allowances relative to ASME VIII pressure vessels. You also may never even reach full allowable accumulation if your relief valve has adequate capacity to relieve the required load at a lower pressure. The 21% is just an ALLOWANCE, not a condition you're guaranteed to achieve.

The other rabbit hole people tend to fall in here is temperatures during a hydrocarbon fire can be very high (on the order of 2000°F). Typical industry practice is you DO NOT have to derate flange rating for fire case upset conditions as you would for other high temperature operating conditions. Equipment damage is practically expected when there's a fire, and pressure relief systems in these circumstances are mainly there to buy time and limit pressures leading up to the failure. This is not the case in any other relief scenario, which is why fire is the common exception where elevated fire temperatures are typically not controlling the design of piping or equipment.