First lets look at another reason that a plant might want to produce fire:
A great many parasitic insects are attracted to CO2 and most organic substances release some amount of CO2 when burned. So producing CO2 may create a small advantage in attracting insects for pollination and/or consumption.
Next how might a plant self ignite:
According to several sources; cotton rags when soaked in linseed oil can spontaneously combust, under the right conditions.
The oxidation of linseed oil is an exothermic reaction, which
accelerates as the temperature of the rags increases. When heat
accumulation exceeds the rate of heat dissipation into the
environment, the temperature increases and may eventually become hot
enough to make the rags spontaneously combust. - Wikipedia
We could extrapolate on that, and picture a plant that could produce a bulb of fibrous material that it would soak in a oil/resin that had similar oxidizing properties. ta-da... Fire!
Now on to sustaining the fire:
The above mentioned bulb could and probably would burn rather quickly. For a sustained fire we would need the stem to act as a tube to continue to feed the, now burnt, bulb with oil without the stem itself burning away.
If the stem was kept sufficiently moist it should hold up for a good long time. (have you ever boiled water in a banana leaf?) So that shouldn't be a huge hurdle.
Continuing to feed the bulb with oil should be fairly straight forward as well, the heat from the flame should create enough suction to keep the oil flowing, or you could look for a more wick like solution.
After the initial combustion the plant would only really need to continue to produce enough oil to keep a small flame going, I doubt a major reservoir would really be needed.
Now what happens when if the flame goes out?
A simple solution here would be that the oil dries and hardens at the end of the stem forming a clot, this would be the signal to the plant to start producing a new bulb.