Does anybody know how to determine the design pressrue of KO drum in a natural gas flare system?

Find your flare tip pressure at max relief rate and add any pressure loss from tip to drum - add margin.

Although a flare KO drum sounds like a drum at the flare, sometimes it might be a local plot blow-down vessel quite a distance away. If your vessel can be isolated downstream or blocked in, you need to look at additional conditions such as the potential upstream pressure against a blocked outlet or the pressure which can be developed due to liquid in a blocked in drum and a fire case.  You can get more information from API RP-520 and RP-521.

If your question is related to an anticipation of an explosive flash-back, there is NO CLEAR AGREEMENT on an appropriate set of design conditions.  First of all, you have to apply operational procedures (purging) to do your best to avoid that condition, but even then, it is not an unknown possibility.

A couple of major Oil companies take the theoretical view that the pressure uplift in a flame front is about 7 times base presure and use 125 psig or 150 psig as a design pressure.
I can personally go along with that on the independent basis that even though the theoretical detonation pressure can go quite high (>40 bars ?) the wave is travelling very quickly so the circumferential stress effects are mitigated by time and strain energy accumulation and the problems historically occur in circumferential joints under longitudinal stress, where the velocity pressure of the wave accumulates, (e.g. bends fall off).  Using a slightly convoluted argument and assuming a detonation pressure which goes as high as 1000 psig, take the conventional 4:1 safety factor on UTS applied by ASME along with the 2:1 difference between circumferential and longituginal stresses to provide 8:1 on UTS for longituginal stresses, which would be a design condition of 125 psig to just prevent total failure.  Experience again shows that vessels designed this way WILL bulge and distort if hit by such a condition.
Just so that we all understand, this is NOT an endorsed condition by any authority and I have NOT rigorously tested the theory, so you're on your own when it comes to responsibility.

The pipeline pressure is 1170 psi. If that pressure is reduced to flare pressure there would be about 30 to 40