Anyway Jayne, I think the Globe Earth Theory for an Eclipse of The Sun is that the Massive  Stationary Sun is eclipsed by the Earth orbiting Moon, which passes between The Sun and Tiny Sun orbiting Earth.  

On The Flat Earth, My Theory and I think it may be the general thinking (I really don't know) is that the Stationary Earth is orbited by a relatively small Sun and Moon, that every so often block our view of one of them.  Although, some people think there is a third "dark" object that causes that.  

Wondering how that might look, I took a flashlight and a coaster into a dark room.  I held the flashlight pointing towards me on low beam, at full arm's length and held the coaster at the joint (elbow), with my other hand, blocking the flashlight 1/2 from my field of view, when held directly in front of me.  I then swung my arm to the right and left, trying to crudely simulate the difference in "eclipse" that I would experience, if I kept my head facing forward and followed the flashlight with my eyes and not my head.  I found that the flashlight was "eclipsed" by the coaster anywhere from 100% to 0%, depending on the position of my arm.  That is what I expected to find.  

So, I would expect that Eclipses of The Sun would look different, from various locations on Earth, when viewed at exactly the same time, with the observer facing directly into The Sun.  However, it also seems to me that the observers angle of view would be different, depending on their location on Earth at the time of a particular eclipse.  So, that might actually compensate, to one degree or another, for the different locations of the viewers.  So, in that case, I'm not sure what to expect;  they may see the same thing or they may not.  

In any case, having been a Flat Earth'er for a while, it occurs to me that our belief that we have to know "everything" is based on a false view of Science.  All we really need to do is observe, enjoy and submit to The Order that God has Created.