Yes, the clay both above and below the clinker are fired. This clay looks like ceramic, looks like busted up pieces of your coffee cup. So the organic debris was buried, covered with sediments, turned to coal through compaction and de-watering, and then started on fire and fired the surrounding sediments.
How did it start on fire? Well coal and organic material create a chemically reducing environment. If Fe and S are present pyrite forms. It is not unusual to find coals with very finely disseminated pyrite in them. Can be abundant but still so fine I need a 30-45X scope to identify the pyrite.
Now if this coal is uplifted, and put into a position where it is above the water table and and subject to infiltration by meteoric waters the pyrite will rust/oxidize. It is actually burning very slowly(oxidizing) and the heat builds up until the coal spontaneously com-busts and is now burning underground.
There is a burning coal on the north side of Rocky Flats south of the city of Boulder, Co.. It is within 10 ft. of the surface and where the combustion gases vent at the outcrop it has it's own little ecosystem. It is warm and damp year round and the assortment of bugs living there can't be found anywhere around there especially during the winter.