How would you make it orbit around a flat earth?
If you plot the paths of most satellites you'll find that they're just traversing the earth either eastwards or westwards, which is a circle around the North Pole. There are various methods for the satellite to stay aloft above the earth. I'll list a few hypotheticals here.
1.) In order to move in this circular path the satellite only needs to take advantage of the common barycenter of attraction which the Sun, Moon, and Stars move around. Provided that the government contractors who put up these satellites got their math right they could cause a satellites be captured geometrically by the multiple system above the North Pole.
2.) An alternative forms of satellite buoyancy includes
lagrange points between the earth and stars, where the satellite is held aloft where the influences of gravitation and acceleration cancel out.
3.) One last possibility is what I like to call the "skipping stone mechanism" where satellites skip across the surface of the atmosphere like skipping stones over water:
In order for this to work - as the satellite hits the atmosphere it must be tilted up somewhat or at least the front edge must be beveled. Otherwise, it can dig its way into the atmosphere, ending its skipping career. Then when the satellite strikes the upper air, it pushes the air down. By Newton's Third Law (For every force there is an equal and opposite reaction force) the air exerts an upward and slightly backward force on the satellite. The upward force pushes the satellite back up into space and the backward force slows the satellite, hopefully slightly.
And if the satellite is given a strong spin it can, like a gyroscope, better keep and maintain its orientation.