Hi Chris,
I'm not sure that there is a reliable way of predicting the pressure from the point of view of stack design.
A detonation is the culmination of pressure piling and that, in a semi-closed system like a flare, is a complex matter of the flame burning down through the various diameters, the hot gas trying to escape at the top and the reflected pressure waves from the closed of the system. Detonations in single diameter pipes are examined by Fike Corp (Chatrathi and Going) AIChE paper 12C 1996 Loss prevention Proceedings, and it's clear there's a run up condition needed. The question for a flare is how much do you screw up the straight pipe run up by using multiple diameters and gas seals and the like.
In any event, if you really pursue the pressure calc it's going to point you towards 700 psig or more.
So, do you design for standard ASME stresses and 700 psig (or more) or do you just say let's make sure it doesn't fail at the disaster case and use the UTS. Bearing in mind that the energy is nearly all longitudinal (failures almost always occur at the elbows and heads) there is an argument which uses an ASME design for 150 psig as being satisfactory.
In the long run, nothing beats careful operations and, although there are quite a number of cases of explosion and damage, there have not been (to my knowledge) any catastrophic failures within flare stacks themselves, even in the absence of a specific pressure design and (probably) 3/8" or 1/2" wall thicknesses.
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David