How significant is air decomposition on formation of nitrogen oxides?
In situations where NOx originiates form $\ce{N2}$, such as lightning or a high temperature furnace, the Zeldovich mechanism dominates:

$$\ce{O2 -&gt; O +O}$$

$$\ce{O + N2 -&gt; NO +N}$$

$$\ce{O2 + N-&gt; NO +O}$$

If a combusting fuel actual contains nitrogen, other mechanisms can be involved.