newengr:
I interpret your response to mean that you are only interested in the amount of natural gas required to sustain the flame required in the flare during the initial venting of off-gas through the flare.
All flares are unique in their design: they are designed for the particular off-gases, flow rates, emergency venting, type of burner tips used, type of controls, etc. Because they are specific to the application, you must refer to the fabricator and their recommendations of the amount of fuel natural gas required to handle the amount of off-gas you will be venting to the flare during start-up. No one can tell you that quantity better than they can due to the fact that they should have all the required basic data for the design and operation of the flare. I am, of course, assuming that the flare fabricator & designer has the design calculations and off-gas analysis and flowrates (as well as the analysis of your fuel natural gas).
Give them a call. If it involves someone like John Zink, I'm sure they'll be glad to consult you on the recommended and safe operation of your flare as well as the quantity of fuel natural gas you'll require at startup.
Art Montemayor
Spring, TX