First of all, the role of archers in pitched battles is often over-stated. Archers were occasionally central to the outcome of pitched battles but those times are rare exceptions, not the rule. To explain why that is, very briefly, it is simply hard to position archers in such a way that they;

a) Are in range to do significant damage

b) Are safe from swift attack from melee troops

c) Are not cut down by enemy skrimishers

It does happen occasionally like at Agincourt, Sphakteria, Crécy and Lechaion but these battles are remembered because they are exceptional, not common. So before we even get to pepper our enemy with flaming arrows we have to overcome the issue of getting to pepper him with anything at all.

Then comes the issue of flaming arrows. Now, firing a flaming arrow is not as easy as you would think. First of all, a flaming arrow is not merely a tar coated ordinary arrow. If you dip an arrow in a flamable substance and fire it, it will go out quite quickly. It is a simple thermal issue, it cools down too fast and dies. Kind of like how you blow out a candle. You have to put the flamable substance in the most sheltered position you can, usually behind the arrow head, you also have to get sufficient quantity attached without drastically altering the preformance of the arrow and even then you have to be careful or it'll go out before it reaches its target. A flaming arrow often had to be fired at much less than full draw and consequently much shorter range to be effective.

So where does that leave us? Well, basically with this: A flaming arrow is the last resort of a besieging force that needs to set something on fire but has no siege engines capable of firing flaming anythings. The battlefield usefulness of non-explosive gunpowder based flaming arrows is highly debatable. More likely your archers would be cut down by enemy archers or attacked by the enemy melee troops before ever they got close enough to fire a flaming arrow.

I can warmly recommend Jim Bradbury's books The Medieval Siege or The Routledge Companion to Medieval Warfare if you want additional information about flaming arrows or medieval warfare in general but if you want really really super specific information about how to light your opponent on fire (a disturbingly reoccuring desire throughout the history of human warfare) I recommend Throwing Fire: Projectile Technology by Alfred Crosby.