This question came to me when I was watching a video about Nuclear weapons, which said that scientists at the time were worried that these weapons would set THE ATMOSPHERE ITSELF AFLAME. So naturally, that got me thinking, what would it actually take to set the entire atmosphere of earth aflame? Is it even possible to set earth's atmosphere aflame? If we can't set the whole thing aflame, then I'll simply ask for the troposphere alone.
The only significant chemical reaction that can occur in the atmosphere is reaction between oxygen and nitrogen. Other components of the atmosphere (argon, carbon dioxide, water vapor) can not be further oxidized and are not in significant amounts.
So, that leaves just oxygen and nitrogen. Those gases can react, but this requires a very high (>2000 °C) temperature. The reaction is hardly exothermic even at that temperature and this "flame" can not sustain itself, meaning it can not spread without external source of heat. So, you can set atmosphere on fire if you heat it to that degree, but by that time everything on the ground will be incinerated.
Basically, just no.
The idea of "setting the atmosphere itself aflame" (via a nuclear reaction, not a chemical one) was raised in 1942 and quickly shown to be impossible. See this account.
About the only mechanism I can think of is the Earth encountering a Velikovskian cloud of volatile hydrocarbon which would infiltrate the atmosphere and form an explosive mixture which would then be set off by just about anything you like, most likely a lightning strike. In effect you'd turn the entire atmosphere into a thermobaric bomb. And since Velikovsky was delusional, and a cloud with the necessary density would condense to liquid almost immediately, and the diffusion into the Earth's atmosphere would be sufficiently uneven to allow reaction with the entire atmosphere at ignition, and generating such a cloud would almost certainly require rewriting the laws of nature, this doesn't seem like much of a threat.