Lighter flints are an alloy of iron and a lanthanide element, mainly cerium. These are extremely reactive metals and it is the exothermic oxidation of small, friction-heated particles ejected by the lighter's grinding wheel which produces sparks. The butane gas flame will exclude oxygen as it heats the flint but when removed oxidation and heat evolution follow rapidly. An oxide layer builds up and slows the ingress of oxygen, allowing some cooling, but the oxide coating then cracks and reaction and heating start again until the metals are consumed and only the mixed oxide cinder remains. Its pyrophoric property was discovered in 1903 by Auer von Welsbach.
Cerium alone is too soft, so iron is used to harden it.
A butane torch is not hot enough to melt the metal and the flame also protects it from oxygen. However, as soon as the flame is removed, the cerium reacts with oxygen, releasing a lot of heat and forming almost colourless cerium oxide, which may even evaporate. The remaining iron, now porous, starts to react with the oxygen to form a special oxide Fe3O4 which is black, crumbly and of lower density than the metal, hence the volume increase. The delay between the first and second glow phase is quite interesting. I suspect it is because the oxygen needs a bit of time to diffuse into the remaining iron.