Massive Fire is a Matter of How Much Dry "Kindling" There Is
I think you and others have got a sense for what sort of things are directly flammable. I will simply add three things.
Is Your Local Biomaterial Dry?
The cases of a single cigarette, candle, etc. causing a massive fire, or even a lightning bolt doing so, are much more common when biomatter, particularly brush, sticks, thatch roofs etc. are dried out, particularly in Summer. Seven major wildfires started in North America in 2018, all during the month of June and mostly late June, though most lasted into August. Of course in some environments the Summer is a period of particular humidity This is fairly common in major cities since they are often abutting a major body of water, especially in eras when water travel was more important. In many deserts summer is monsoon season.
To a D&D game this is mostly relevant in whether the DM can "realistically" say fire spreads or does not spread when they have already extensively discussed weather, environment, season, etc. If they have described days of heavy rain, for example, saying the whole town burns down is substantially less fair then if they have described days of the sun beating down.
Thick Pieces of Wood Usually Don't Directly Catch Fire, but Burn Long once They Do.
As anyone who has ever started a campfire can tell you, it takes a great deal more sustained fire to light up a log on the fire than kindling, which is the whole point of kindling. The wooden beams in many buildings as well as substantial trees generally require more flammable materials burning around them before the catch fire, at which point they then potentially burn for a long time. From a DM perspective, the more tapestries, furniture, and other biomatter based things around that can function as kindling at some level or other the more likely that a vast, general conflagration results.
And Let's Discuss Medieval Construction
Presuming one is using the typical D&D pseudo-Medieval, quasi-European setting, it is probably worth discussing the construction methods of the period and place generally for anyone interested. I am not an expert on historic construction but I do have a masters in Medieval and Renaissance history, which means lots of anecdotal knowledge.
So far as fire goes, the prevalence of thatched roofs was the most devastating part, as it was both most easily ignited, and the part closest to one's neighbor (in places where people lived near each other) Aside from the material being inherently flammable it likely has the sun beating down directly upon it every sunny day making it nice and dry in the right season. Wood is of course something that burns, though the thick wood supports don't usually ignite easily without a substantial fire near them. But, between the thatch and the small sticks often used to infill between wooden wall supports, your average medieval home lights up quite easy. Also be aware that in many places they were not primarily made of wood but rather what we would view as hovels made of sod, wattle and daub, etc. which I believe are all still more easily flammable material in a dry season, and these materials would often be the sorts of things infilling between beams in a wood framed structure as well. In a "nucleated" village where everyone has homes next to each other this was likely to be a catastrophe for the whole community, but keep in mind that as often as not the buildings of a village were spread out around the fields. A field of wheat, by the way, is also nice and flammable when dry.
As for stone (or brick) buildings (usually churches, fortresses, etc), they were still in danger of substantial destruction so long as there was sufficient flammable materials in the roof, supports, floors, furniture, decorative carvings, tapestries, etc. Between some stone and bricks melting to some degree in an intense fire, and the stresses of attached wooden support beams collapsing, many walls were toppleable. While stone structures are likely to survive a fire in a gutted form, other than thick fortress defensive walls no man made structures are immune.
So basically a typical urban, village, etc. scenario is that roofs and furnishings catch fire, if there is a lot of this to catch fire then after a while this spreads to wooden structural elements and neighboring buildings, and eventually (possibly hours later) there is no longer a building or a gutted stone structure with a few walls or towers collapsed.
There were no fire departments, but note that there was a firm tradition of the whole community dropping everything to do their best at trying to stop a fire by what limited means were available, something which actually may make for a more interesting element of rpg adventure than the actual fire.