I typically use fire arrows when I want to keep a continual barriage of arrows hitting the enemy, rather than for my archers to expend their reserves in a short amount of time, which is usually what happens when you use normal arrows. This is particularly the case in siege battles, whether defending or attacking. Having the ability to cause fear with your flaming arrows whilst your infantry and cavalry attacks your enemies is a very good thing, increasing the chances of creating a chain rout in the enemy's ranks, especially at chokepoints. Also the AI is often stupid enough to leave elephants in range of your archers on the walls at the start of a siege defense, so you can use fire arrows on them and laugh as they run amok and kill loads of your AI's stupid troops!