In commentary about football plays, you sometimes hear references to players being “in the flat”. This seems to refer to a region close to the line of scrimmage. Is there a more precise definition? And why is it called “the flat”? I would hope that the whole field is flat, no? 
It’s called that because the receiving route traversed by running backs to the area is “flat.” That is, when drawn on an overhead view of the field, it’s pretty much a horizontal line.
Right, line of scrimmage forward about 10 yards, and from the hashmarks to the sidelines (so not the center of the field.)
https://en.wikipedia.org/wiki/Flat_(football)
I don’t know the answer to your ‘Why’ question.