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: 
It's science-based.

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> But how plausible is that, biologically speaking?
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Nope, for each additional 10°C temperature, the speed of chemical reaction roughly doubles. Between, say, 40°C ambient for normal life to a 600°C for a puny fire temperature, you have 256 difference in the chemical reaction speed\*\*. There's too much of a difference for the life forms to be based on biochemistries close enough to evolve one from the other.

\*\* [Citation](https://courses.lumenlearning.com/introchem/chapter/factors-that-affect-reaction-rate/) `Raising the reaction temperature by 10 °C can double or triple the reaction rate. This is due to an increase in the number of particles that have the minimum energy required. The reaction rate decreases with a decrease in temperature.`

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> Is there a better approach to creating a permanently burning forest ?
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Your only chance, by direct evolution in hot conditions.
**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.