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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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.
Biology already knows plants that got adapted to periodic fires. These include either fire-resistant trees that just do not catch fire because of some non-burning composition or seasonal plants which get burned but keep roots and/or seeds intact so to re-grow.

A permanent forest fire with burning trees is likely impossible, because it would require much more energy than can be produced.

So, you are confined only to a choice of either periodic, seasonal fires or fires with fuel supply other than trees.

That fuel supply can be natural gas, petroleum, underground coal or peat deposits, or gas produced by microorganisms on swamps (burning methane is common in swamps, producing "lights").

The underground peat deposits can burn for years in Moscow area, even under snow, producing smoke. But, of course, this does not mean the trees are burning all that time.