The following articles written by two researchers Firestorms and flaming tornadoes: how bushfires create their own ferocious weather systems and Firestorms: the bushfire/thunderstorm hybrids we urgently need to understand provide information on the dynamics behind firestorms and the formation of pyrocumulus clouds and the associated dry lightning.
Following is a summary of those articles and the conditions that lead to dry lightning from pyrocumulonimbus clouds.
Not all bushfires lead to firestorms. If a bushfire has sufficient area the upward movement of air causes the fire to interact with the atmosphere above it and form what is known as a pyrocloud. If in addition there is an atmospheric instability then this process leads to the formation of a pyrocumulonimbus cloud . Normally in meteorology we are taught of heat radiating from the ground but in this case the upward movement of air is due to the heat emanating from the fire.
Again from mesoscale meteorology one hears the word "downdrafts". Similarly in this context the appropriate word is "downbursts" and these are vertical drafts of air that hit the ground and move about in all directions. The unsettled conditions cause embers to carry over large distances.
These firestorms produce dry lightning that potentially can spark new fires that may end up creating a larger flaming zone.