Hi Thorlake,
I imagine on the regular Flat Earth model with the North Pole at the center of the earth, the sun is simply close enough to your northern location at night so it can be seen during the summer 24/7.
On another map like mine, where Antarctica is the center of the Earth, and sun is farther away from the Northern edge at night, to far to be seen physically, I believe the Sun's reflection wraps around the atmosphere at night so what your seeing is a reflection of the sun, not the sun itself. See the image below:

Notice the main light on one side of the magnifying glass and a less bright reflection of the same light on the other side - as well as a third reflection but you see its possible under the right conditions-.