Flat shading is in transition. In the 2.80 Blender beta exporter, vertices are flat / smooth shaded on a vertex by basis, like they are rendered in Blender.
I can see by the producer tag of your .babylon file, that you are using 2.79. In that case, just add an Edge Split modifier on the mesh. For more info on shading from the Blender exporter & how it changes for 2.80, see.
You can also force flat shading once in BJS, but I am not going to look that up for you. It is not hard.