Exploring the rafters until you manage to get behind the walls of the prison, you can find the breakable walls of the cells. Using a bludgeoning weapon, in my case an adamantine mace that I procured from the Grymforge earlier, I broke the back wall of the right most prison cell before running over to the left cell and breaking that, this results in most prisoners being by the boat before a guard noticed and combat starts. Take those guards out before reinforcements are called, which isn't so hard, and the prisoners will leave via the boat.
Additionally, if some prisoners get to the boat before combat starts, it seems like the boat is not chained up. Not sure about the specifics of that trigger.