The most amusing thing to come out of flat earthery lately is the Pacman Earth.
This theory states that the Earth is flat, and we are able to travel 'around' it in the same way that Pacman moves instantly from the top to the bottom of the screen, or from one side to the other. In the Pacman game, this is achieved by using a hypothetical higher dimension, in this case the third dimension.
As it happens, this has been well studied in the field of mathematics known as topology. Topologists even have a name for this higher dimensional topology, which shows that the flat earthers are close to exposing the truth.
The name of the topology?
It's called a sphere.