There are many different paths leading to many different ways to escape fort joy.
1/ Escape by boat: You need to receive " Withermore Soul Jars" quest , so you can unlock a secret underground hatch by interacting with the shrine of seven in Fort Joy. Its a shortcut to the underground dungeon , once you down there , help the fallen magister and he will help you escape.
2/ Escape through a sewer: Its also located in the underground dungeon , in the tortune section. You will have to fight 3 meat golems and a maniac then escape through the sewer on the left.
3/ Escape through a habor: Its located in the area just after you go through a small secret cave in the beginning. There is a small gap between Fort Joy and the area which you can use any teleportation/jumping skills to get over. The battle at the habor is in your favor because you are the one that start with high-ground advantage.
4/ Escape by forcing your way through Fort Joy: You will get a little "help" from a Paladin inside the Fort. After the battle you can hit the switch nearby to lower the bridge then escape.
5/ Escape through the Magister room: You might need to finish the Muderous Gheist quest , Yarrow will give you a key to unlock the yellow door just to the right of the big guarded gate. Or you can picklock it. A fight awaits you pass that room. After the fight , look for a small room filled with wood boxes/barrels , remove them and you will see a way leading to the forest.
