Acceleration requires energy to make it happen. Gravitation does not.
What does gravitation require to make it happen, then?
It is a VERY common misapprehension that a FORCE requires ENERGY. It does not. When you attach a magnet to your refrigerator, it stays stuck there forever without "running down" because it's not consuming any energy to be there. When a book sits on a table, the gravitational pull of the book on the Earth doesn't run down - and the equal-and-opposite force of the table pushing up on the book doesn't require energy either. The book sits on the table without either consuming energy.
Gravity is like magnetism in that regard - both produce a force without energy expenditure.
HOWEVER: "Work" is "Force-through-a-distance" - and "Work" is "Energy". So as soon as something moves - energy is required to make it happen. So if the Earth is physically moving as it accelerates upwards - then for as long as it accelerates, some energy is being expended somewhere.
With gravity - if you LIFT a book to some height, then you're providing energy with your muscles to move the book. The book retains that energy as "gravitational potential energy" - and if you drop it, that energy will turn into kinetic energy as the book accelerates towards the ground - and then into heat and sound energy as it impacts.
But your Flat Earth is being accelerated continually - accumulating more and more kinetic energy - which DOES require some input of energy from someplace.
Now - you might argue for magic - or some "unobtainium" that carries limitless energy within it...but you DO need some kind of an explanation for where this energy has been coming from for the last god-knows billions of years.