Hi and WELCOME!
Oil-fired dryer?
STOP THIS MERRY-GO-ROUND RIGHT NOW! LOL
PLEASE describe the burner, and does the machine have a fuel storage tank within or like today's oil burners, is the oil supply just piped in?
Since early oil burners were not the cleanest burning and did not have complete combustion, carbon and soot and odors would in theory be a problem. I am guessing, therefore, that a heat-exchanger would be expected here. (Like a frigidaire filtator that used room air to cool the warm moist air that circulated though the clothes and drum. The two air streams did not mix).
I am theorizing, then, that cool dry clean air is heated by passing over the air-stream of the combustion, but the two air flows don't mix. The dryer then may have had a vent for the warm moist air and another for the products of comustion (or perhaps hey were combined before exiting the machine).
I would personally kiss your feet for pics of the guts of this dryer.
Thank you so much for posting and sharing you insights and discovery.