You could theoretically place a motion-log device inside a satellite in order to track how the satellite makes its way round Earth; whether it follows a widened orbit pattern as a result of the flat earth's wide circumference and small height, or the usual geosynchronous spherical band of orbit. This could be backed up with a camera similar to Hubble's, albeit less expensive and massive, and a 1/frame per 15 minutes video recorder.
That way, near-infallible evidence as to whether the earth is round or flat will be provided.