All you have to do is record the orders to the helm.
Keep the land to port and if you always steer to starboard you're going in a circle.
If you keep the land to port and you always steer to port you get a different circle.
Yes, but the latter circle keeps running aground.
Really, to prove their Flat Earth hypothesis, all they need to do is start sailing east or west along the Equator without turning. If they eventually hit the artic or antartic, then their hypothesis is proved. If they stay on the equator and never reach the arctic, then their hypothesis is disproven.