Depends what you mean by a flight sim. The first flight simulator that was designed to help to teach pilots was actually a mechanical apparatus - called a Link Trainer. It was built in the late 1920’s. Of course, it did not have any graphics but it was only a simulated set of flight controls that were attached to a mock airplane, that responded to the controller movement.
But yeah, as others have pointed out, the first home computer flight simulator was probably subLogic’s (Bruce Artwick’s company) Flight Simulator, the precursor to Microsoft’s long running series.