Introduction
A major difference between RE and FE is the alignment of our magnetic poles. RE has two points, FE has a point and a rim.
So on a round earth, your south pole on a magnet will point to the earths north pole.
This leads to something that is easily overlooked about FE. Because the south pole is a circle on a flat earth, there are many places a compass is attracted to. If you are standing on the earths north pole there is an equal pull from the south pole of the earth in every direction. However, as you move away from the north pole, you get more points on the south pole in the opposite direction. This means that if you add up all the points of the south pole rim and their vectors, you will have a vector that goes through the north pole. These many many south pole points are much more than one north pole point.
So on a flat earth, your north pole on a magnet will point to the earths north pole. (Even though it is really pointing to the net vectors of the south pole rim)
Experiment
Things you will need:
Kitchen sink (it can stay in your kitchen)
Bowl
Rectangular magnet, labeled for north and south
Fill the sink with water.
Place the magnet in the bowl.
Place the bowl in the sink, so that it will float.
Conclusions
If the north pole of the magnet points north, the earth is flat.
If the south pole of the magnet points north, the earth is round.