To unlock the Fire on Water trophy in Assassin's Creed Odyssey, you must first purchase and download the second episode of the Legacy of the First Blade DLC. You must then progress through the main quest, finishing Theatrics and Espionage and then Tides of War. The Flamethrower will be automatically equipped at the end of this quest.
Now simply set 10 enemy ships on fire with the flamethrower (face the camera towards the front of your ship without holding L2 and hold R2) and after the 10th ship is lit, you will unlock the trophy. It's not enough to just get the flamethrower on it -- the fire icon gauge needs to fill up and put the ship in an "on fire" state that limits its movement and firing capacity.
It's worth noting that you will have to destroy several ships in the course of the main quest anyway, for example in the mission "Persian Puppetry".