As indicated by JKEngineer, thermal temperature calcs based on heat transfer and radiant imput are the usual manner in which this is done. I have some formulae in a paper which I would be glad to send you if you drop me an email to flareman_xs@netzero.net.
I have to caution that this calculation has to be very "iffy" because the radiant profile from the flare flame itself is almost a "wet finger" calculation and you have to make so many assumption about emissive surfaces and convective conditions in the temperature calcation that your final condition is only accurate (maybe) +/- 50 degrees (C or F .. doesn't matter). Then you realise that there are a lot of other conditions you haven't investigated which can give you other temperature ranges.
Any shield dramatically reduces the radiant load because the flame is radiating based on a mean temperature somewhere around 3000 degF whereas, behind the shield, you can only receive radiation based on the shield temperature which is much less.
The biggest real world temperature concern has to be exposure time. The thermal mass of much (metal) equipment slows down the temperature rise so that it can easily tolerate high radiant profiles over the short term but it will achieve a high equilibrium over the longer term (several hours), and that's when the problems arise. Plastics and electrical wiring suffer much more quickly because they don't have the ability for internal conductive transfer of heat away from the heated face.
With storage tanks you are probably most concerned that exposed metal edges which are not convectively cooled by the wind, can reach temperatures which are incedive for the vapors in the tank. I'm not convinced that anyone has successfully made this calculation and, in my experience, most people go with about 1500 btu/sq.ft_h as a limit because it probably can't generate temperature above (about) 300 degF even in the extreme case and it is also the "safe" personnel limit (that's a whole other story).
Good luck
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David