User blog:GreyFang82/Igniting the Atmosphere: According to the US Government

In this (Now declassified) paper written around the time The US were testing Nuclear weapons for the first time, multiple scientists asked if using these bombs may ignite the atmosphere. In response calculations were done to find out the minimum amount of energy that needs to be released to start a runaway chain reaction that would slowly burn out the earth's atmosphere.

On page 17 the scientists give out the minimum amount of air that needs to undergo ionization for the effect to happen and give us the energy value of 7.5 x 10 ^ 32 of MeV or Megaelectricvolts. Doing the conversions that would equal about 1.20163247 × 10^20 joules of energy, about 28 gigatons of tnt, or Island Levels of energy.

Now this doesn't give the amount of energy is needed to ignite the entire atmosphere at once, but this can be used to give the minimum to start a chain reaction and give overtime feats of this a solid backbone.