Do you mean to say of magnetic fields in general or simply the magnetic fields of celestial bodies?
Ah, my apologies for being obscure (and wrong) on this point. I am talking about the magnetic field of celestial bodies. In this discussion, we're talking about the magnetic field of Earth as a whole (the one we can use with a compass.) The magnetic model for a flat earth must conform to the magnetic field of Earth as a body (round or flat).
They would only be vertical near the poles. Which is the same way as the RE.
However, there are horizontal lines at lower latitudes in the real Earth, and not in the situation you are describing. All the lines would be vertical because they would be going up and away from the Earth, wrapping around the sides of the Earth, and going underneath the Earth.
About time you understand.
I've understood all along.
The aurora happens during the day as well. It just gets washed out.
That is not the point though. The point is that given the shape of the magnetic field under the flat earth scenario as you suggest a night time aurora will not happen. Thus, we should never see any auroras given the model you describe.
There are numerous mag. fields on earth, and the Earth's field is one of them.
Earth's field is the relevant field to this discussion. Again, my apologies for misstating this.