Question: In my world, I'd like to place a region of permanent forest fire, but I'm having trouble coming up with the minute details of the biome.

For example, my first idea was that it started when a lush, humid forest was exposed to a volcanic eruption, followed by a permanent but slow lava flow, lasting long enough that some plants have adapted and evolved into flora that relies on the constant fire and is itself so slow to burn it can outgrow whatever is lost to the fire.But how plausible is that, biologically speaking?

What is a better approach to creating a permanently burning forest?

Answer: 
You can't have traditional trees they're too slow you need something that grows far faster, probably faster than [Bamboo](https://en.wikipedia.org/wiki/Bamboo) or even [Kudzu](https://en.wikipedia.org/wiki/Kudzu), something with a growth rate in the 10s of metres a day range, more importantly 10s of kilograms per day. I don't think osmosis allows for absorbing, moving and just chemically processing that much material but lets go with it. What is this plant going to be like:

* It will have a metabolic focus on producing thick porous [bark](https://en.wikipedia.org/wiki/Bark_(botany)) that starts with a high water content and dries and burns and crumbles off while being replaced continuously. It will be the bark rather than the stems of the plant that smolder continuously.
* The tissues of this plant are going to be high in silica and chromium as flame retardants.
* It's roots are going to be deep and extensive and exude acids to mobilise growth nutrients, these root adaptations exist individually in nature but not in any one plant that I know of.

All of these adaptions do exist in nature; Oak trees survive grass fires in meadows by having a thick spongy bark. Willows have high silica in their wood making it slower burning, which is not why it is there but is a useful side effect. Many grasses in fire prone environments have deep roots to survive burn over. Clover roots exude acid primarily to balance their pH in light of nitrogen fixation but it has the side effect of mobilising nutrients from dissolved soil particles as well.

Such a plant won't give you a big flashy crown fire but it could smolder continuously pouring smoke and ash into the environment and burning anyone who ventures that way.

I reiterate that ***I do not believe*** that this is within the reach of the biological systems we understand and share our world with but maybe if it smoldered slowly enough without burning out it could work.
**Fire loops around the globe**

Your planet has its landmass as a band around the equator.
(or, alternatively, there's [almost] no open water, poles are covered in snow, leaving only the equatorial zone available to the biomass)

Somehow, there are no large rivers.
(plants still need to get moisture, and there's evaporation, which means there ought to be rain- or snowfall, which usually means runoff, but fires tend not cross large bodies of water... figure this out).

The equatorial zone is dry-ish, and e.g. typically covered by grasses.

The fire started (magically in only one direction), spread the entire width of the equatorial zone, and continues to burn, e.g. westwards.

By the time the fire has reached it's origin, that part has already sprouted new mature (and dry) grass, with seeds either preserved deep in the soil, or spread by wind, or spread by birds or even migratory animals.

Thus the fire continues to burn in a circle around your planet.

The long-lived plants died out, what remains are grasses and maybe shrubs.

The plants have therefore evolved to live in this cycle, and so have the insects and the animals.

P.S. some math

Fire boundary speed: 10% of wind speed (<https://link.springer.com/article/10.1007/s13595-019-0829-8>)

Typical wind speed: 10km/h
(<https://sciencing.com/wind-speeds-tropical-rainforest-23367.html>)

Thus, for a planet the size of the earth, the fire circumnavigates in ~4½ years, leaving enough time for plants to germinate, go through several life cycles and accumulate large amount of stale, dry biomass.