Fire arrows were mainly used for lighting structures on fire. They were not literally flaming, but were rather just heated up so they are more likely to start a fire if they get lodged into a wooden structure. If they had open flames, it would be put out by the air movement around the arrow. They were primarily used for shooting over walls in huge amounts to possibly start fires behind them and to annoy/distract the defenders. It is a lot easier to light wooden structures on fire with torches if you can get closer to them, and preparing fire arrows takes a long time and would be hard to do on horseback. Also, they are not very useful for shooting at people when compared to normal arrows, and might actually be less damaging because the heat could cauterize the wounds they make. Its not like people are lit on fire for a few seconds and receive burn damage.