So what is the main problem with the acceleration theory, (besides the fact that we have pictures of the earth from space), if this hypothetically was the way that gravity was generated, would we still have an atmosphere?
There are 2 main problems.
The atmosphere would depend upon what is at the side of Earth.
If you had a magic wall around the edge that can keep the atmosphere in, with the acceleration acting as a cap for the top then the atmosphere is kept in. It would also work with their magic dome.
It would only be an issue with nothing at the edge allowing the atmosphere to flow off the sides. And that is something to address regardless of what makes things go down, and is only eliminated by having Earth as a sphere or an infinite plane so there is no edge.
So I would say that part isn't the main problem for the idea of acceleration, but is an issue that needs to be addressed for a finite flat Earth.
The simple big problem to appeal to is "why/how?"
Just what is causing this acceleration?
Some flat Earthers call it universal, because not only is it accelerating Earth, it is also accelerating everything above Earth, like the sun and moon and stars, so they stay aligned with Earth so we can still see them; but for some reason not us if we jump above Earth.
The far bigger problem is the variation in g across Earth.
g is not constant. It is not 9.8 m/s^2 all over Earth.
It varies as you move around, with both latitude and altitude affecting it, as well as the distribution of matter inside Earth (because it is actually caused by gravity).
At the equator, it is lowest at ~9.78 m/s^2.
At the poles it is highest at roughly ~9.83 m/s^2.
Importantly, this is a difference of ~0.05 m/s^2.
And unlike the overall acceleration, there clearly is a reference here.
An observer at the equator would see the poles appear to rise at a rate of ~0.05 m/s^2. After 1 day (86400 s) this would result in the north pole rising to a height of 186624000 m, that is ~187 thousand km.
So if it was coming from Earth accelerating, the difference in acceleration over Earth would tear Earth apart in less than a day.
After 6 hours, it would reach over 11 thousand km, meaning the north pole would be higher than the distance from it to the equator.
Now you could ask about relativity and its effect on that, but after a day, the north pole would only be going at a speed of roughly 849 km/s, which is less than 0.3% of the speed of light; or ~4.3 km/s with the full relativistic equation giving 4319.96 instead of 4320. So this is not going to be a problem at all and the argument above holds.