Ships of the era were almost entirely made of wood. Was fire recognized for its destructive potential in battle and was any weapon system developed for its delivery?
We know about Greek fire, an early form of napalm, used by the Eastern Romans and fire ships used during the Battle of Red Cliffs, for example. Ships’ armament was mainly smoothbore cannon, but would large-scale weaponization of fire have been effective in burning down enemy ships?
Fire was most certainly recognised - and used - for its destructive potential. Sailing ships of that time were more vulnerable than earlier ships, due gunpowder on the gun decks increasing the flammability of the ship, and gunpowder magazines making the ships potential bombs.
A wide range of delivery methods were used:
Simple but short-ranged: hand-thrown ceramic incendiary grenades
Heated shot: take a regular iron cannonball, and heat it, preferably to red hot, before loading the gun. Simple to do - just have a nice hot fire/furnace next to your gun. This is obviously a serious fire hazard on a gun deck, so heated shot was mainly used by coastal defence forts against ships.
Molten shot: heated shot on steroids! Rather than just heating an iron cannonball, take a hollow iron cannonball, and fill it with molten metal (molten cast iron AKA pig iron was usual). The advantage over conventional heated shot is that when the iron cases breaks open, the hot molten metal goes all over the place, and is more likely to start a fire. Again, this is something better used from forts than from ships. However, right at the end of your time period, the British Royal Navy adopted it as a shipboard weapon, with HMW Warrior being equipped with suitable furnaces in 1860 (and then in 1869, the RN declared molten shot obsolete).
Carcass: incendiary grenades shot from a cannon. Take a casing that will survive being shot from a cannon, and fill it with pitch and/or other flammables. Ignite, load into cannon, and fire at enemy. European use appears to have begun in the late 17th century, and continued to the end of the Age of Sail.
Shell: your basic explosive shell. During the Age of Sail, these were a round casing filled with gunpowder. A timed fuse was lit, the shell loaded into the cannon, and then fired at the enemy. While much of the effect was the blast from the explosion and the fragments of the casing, the explosion presented a serious fire hazard, so it can be counted as a part-time incendiary weapon.
Fire arrows. Fire arrows had been used long before the Age of Sail, but cannon allowed larger fire arrows to be shot further. Cannon-fired fire arrows were popular in East Asia, seeing use in Chinese, Japanese, and Korean ships.
Fireships. Take an old ship, and fill it with gunpowder and flammables. Light, and launch towards a downwind enemy. With good luck, the fireship collides with an enemy ship and their riggings tangle. With good timing, the fireship explodes (due to the gunpowder) in the middle of the enemy, showering them with burning stuff. Especially effective if the enemy can be caught by surprise in harbour or some other anchorage. Less effective in open sea, since the enemy will wisely avoid the fireship. However, even then they can be very useful even if the enemy completely avoids them, disrupting the enemy formation.
Further reading:
Peter Kirsch, Fireship: The Terror Weapon of the Age of Sail, Naval Institute Press, 2009.