To help imagine it and my inspiration, it's basically similar to pictures from Abrahamic religions with burning trees like this one. They can't speak though, they are just trees or plants that are burning.
Also, I know about (real plant) eucalyptus trees, which can generate easily burnable toxic oil to create forest fires in order to eradicate competitors. I also know they have thicker or secondary/multiple layers bark/wood and hidden stems in their cores to survive the forest fires they create. They can even shed their bark to be carried by wind in order to create new fires spot. Also, banksia, which need fire to reproduce. So, my fire tree is a bit similar to both of that except it's literally on fire forever until its death. It generates the fire like its leaves. It's not necessary for the trunk/wood or other parts to be on fire, though.
I also think my fire trees burn themselves as an extreme way to create rain, similar to how rain forests do to cool down and get water from the heat they generate (they are not on fire though just hot, I don't quite understand how it work so correct me if I am wrong regarding this). but I also don't want the fire to go away until the tree is dead. Also, the sudden extremely different temperature due to rain may can harm it, even if it can withstand fire. so i am not so sure about this method can work for my tree.
I might use this fire tree for burning its competitors, scaring away anything that wants to eat/destroy it, or spreading its seed. But I can't figure out how they gain energy, is there a way for such tree to gain energy from the fire? What kind of modification/evolution would trees need to do so? Since photosynthesis doesn't seem to be the way to go (correct me if I am wrong, and it not necessarily they get the food or energy from the fire either).
I don't know what kind of region/environment or weather/climate it is yet outside of that these trees only exist on an isolated island, although originally I was thinking something like a tropical forest near the equator. Feel free to suggest a better region to suit such a tree.
Modifying the entire world to make this tree exist (such as filling the entire planet with methane or eucalyptus oil vapor or other easily burnable material) is out of the question, because my world is habitable planet similar to the earth. It is, however, acceptable if a modification to achieve an environment for such a tree would only exist in that isolated region.
It is also acceptable if the fire it generates is not actually harmful or can burn someone; I believe there exists a chemical that has fire that has a lower temperature that can not give burns - something like the fire in Jackie Chan movie in Karate Kid. If possible I prefer the harmful fire though, since I need to burn other trees to make only this kind of tree dominate the island. Besides, such harmless fire is less cool.
It's also acceptable if they need to have a short life to achieve this, but if possible I want it to have a long lifespan like a common tree.
It also not necessary for the fire to burn out or be gone after the tree dies though.
Also if possible, I don't want the plant to be a carnivorous plant in order to get food or energy, although I can imagine how to apply it as that. That is out for this question.
Feel free to correct my grammar and change my tags to the appropriate ones.