Because the same force that is accelerating the Earth is accelerating the sun and moon.
It could be argued that under the flat earth model, our entire planetary system—earth and its moon, the sun, and Mercury, Venus, Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto—could be moving as a unitary system, that is at the same fixed, relative distances from each other. The plane of orbit of each would have to be separated sufficiently (millions of kilometres?) to avoid any collisions caused by their differing geometric paths, and there'd be some problems isolating some unknown phenomenon that caused them to rotate independently of our own sun—maybe a massive sphere of undiscovered dark matter with a gravitational attractive force exactly equal to, or greater than our sun's?
It could also be pure chance that our earth was first attracted to the sun, whilst the other planetary bodies were first attracted to this mass of the dark matter. Or possibly the earth originally possessed too little kinetic energy to escape the sun's pull, whereas the other planets possessed sufficient energy to escape our sun's gravitational pull, but not the (possibly) larger mass of the dark matter?