As a Michigander, I have to emphasize that this is a Michigan song. The Flat River is a tributary of the Grand River in Michigan. The Grand River starts near Jackson in south-central Michigan, and flows into Lake Michigan at Grand Haven (which as a wondrous pair of lighthouses). I grew up near Grand River Avenue in Detroit, not knowing that the Grand River was far, far away (you may have heard of Grand Rapids, though...).
-Joe-