Assuming that your map is in something like the Equirectangular projection (the special case of Plate Caree where it's twice as wide as it is high), then the N/S distance on your map is the true circumference of the sphere. Your map is just about Earth sized, as you mentioned when you said that it was 25200 miles from pole to pole.

The difference in size on Earth between the equatorial and polar measurement is due to the rotation of the planet and the mantle being a semi-plastic, deformable material (the equator is going about 1000 mi/hr). The difference between a perfect sphere and the oblate spheroid that is the Earth's true shape is about one part in 300, or not enough to be noticed for most whole-world maps.

The biggest problem with a flat map is that you can't use a flat ruler to measure distances. The horizontal scale on your map varies by 1/cos(latitude): the scale is 1 at the equator and infinite at the poles (spreading a single point out across a whole line segment). For measuring distances with a ruler on a flat map, you need a relatively local area and a projection centered on the middle of your area of interest. https://en.wikipedia.org/wiki/Map_projection is a good starting point to learn more about map projections.

There are many pieces of software that will convert your map into another projection, including G.Projector ( https://www.giss.nasa.gov/tools/gprojector/ ).