Two different frame challenges to all of this
Q: What non-magical conditions of topography and climate would a forest habitat need so that it would not propagate forest fires, and trees will also thrive, so fire-wielding fey can live safely?
A: You can't find a suitable forest, or.. you won't need to
FC #1 Unless you invent new trees, fire is unsafe in any forest
Trees consist of wood. Lots of carbon. Trees leave their remains to dry out in summer, which will rule out culture- and occidental forests. They'll go up in smoke. In the tropic, you'd have rainforest, which is less vulnerable to occasional fire, but these creatures add more fire to the environment, after they arrived. The behavior of humans can be compared with that: we are also a relatively new species and we also use fire. Intentionally or unintentionally, people burn down rainforest. To prepare for agricultural use, people burn their land and the fire reaches the forest..
Rainforests are increasingly susceptible to forest fires today due to
degradation from selective logging, fragmentation, and agricultural
activities. ... Under dry conditions these agricultural forests can
easily spread into neighboring rainforest.
Holes in the forest will expose more forest to the sun. The issue with these "fire pathways" created in a rainforest: it will increase vulnerability for future fire, which can again seem small, insignificant..
Small fires are not unusual today in the rainforest. Even in "virgin"
forests, fires may burn across hundreds of thousands during dry years.
While these fires may seem innocuous, with flames reaching only a few
inches in height and having virtually no discernable impact on trees
or the canopy itself, they cause insidious damage: in passing, the
fire sets the path for recurrent fires and subsequent forest
loss.Once-burned forests are twice as likely to be deforested as
unburned forests, largely because the initial fires—however small—thin
out the canopy, allowing more sunlight to reach the forest floor,
drying out lead litter and setting the stage for future fires.
So.. even when a forest is inherently protected, by moist, or by evolutionary adjustments, it will remain susceptible to small damage, causing more damage, etc. This process is called a feedback loop.
Some trees adjust to fire, like the ones described in one of the two main answers in this topic. In that case the issue is, evolution is a matter of millions of years of adjustment to a specific environment, in this case the probability of lightning to occur. The trees have only adjusted to fire that occurs naturally. Human agriculture is a new phenomenon, these dragons or "fire elementals" are also new.. Forests decline, your dragons won't help. Better house them away from trees.
FC #2 Don't worry, nothing special is needed, let them live in the forest
At first, when I read the question, I wondered what was meant with the word "elementals" and "fey". The opener is vague about these creatures, in fact they could be animals, savvy aliens, or fantasy creatures.. There's a lot of freedom left, from our viewpoint, to define these "fey elementals".
Try a few cases, posing no problem at all
Suppose they're aliens
The easy one. A bunch of intelligent alien "fire elementals" landed their ships on Earth and colonized the forests. They consulted Vogon Poet for a place to live. They breath fire on a regular basis, but there actually isn't much to worry about. They can look after themselves, understand the vulnerability of these forests and prevent damage. They chose to live there, why destroy it ?
Suppose they're animals
There may be no issue at all. Take a forest animal as an example: the beaver could do considerable damage to forests, by logging at will.. and damaging lots of trees with their nasty strong teeth. But beavers don't do that. They build dams only to protect their dwelling and put the water where they need the water to be. Why would dragons, or any other fantasy animal behave differently ? After a few generations, they'll have their mating rituals (fire parties) in an open space somewhere, or outside the forest. Or.. they simply have learned already, how vulnerable this "wood" is, for fire. They can make fire, so they grew up with it.
Avoid projection, these elementals are unknown creatures
The worries of Vogon Poet, my above absolute nogo-scenario and most answers are actually based on projection.. as a human, I imagine a human using fire carelessly and I stick the same issue on these dragons. But.. is it valid to assume that ? will they behave like apes, like we do ? that is... consume a forest environment, drop your shit and move on ? That's what apes do.. and still do.. but why shouldn't these dragon creatures behave more balanced and adjust their behaviors to their environment? They are used to their own fire..