The thing about the tides is, because the moon orbits the earth, the tides follow the moon in one direction. For example, tidal levels would move from East to West, like a gigantic rolling wave. This is because that's the path the moon traces overhead, and both sides of the camp agree to that. So, in a round earth, the tides follow the path of the moon.
Rowbotham's sloshing analogy is a fallacy because that would mean that the tides would go from East to West, then West to East, reversing direction each day, which they do not. Therefore, the evidence of the tides does not add up to the predictions of the Flat Earth model.
I've seen other Flat Earther's admit that the moon does in fact cause the tides due to gravitation. However, Francerty and the Engineer like to point out that there is no force of gravity, and the acceleration of the earth through space is what causes the sense of gravitation, as inertia and gravity are indistinguishable in some cases.
This is impossible for several reasons. First, that would mean that the other stellar objects cannot exhibit gravitational forces either, meaning that the moon is not responsible for tidal action. The earth and the moon are both matter (moon rocks have been carried back to earth, and for the more die-hard conspiracy theorists, we have found them falling Earth as well) so one can safely conjecture that they both have the same physical properties. A blueberry pie and a strawberry pie are different, but they are both pies with crust and sweet, sweet filling.
Next, the constant acceleration theory is directly at odds with several well-established mathematical principles, such as General Relativity and the laws of thermodynamics. In relativity terms, a constant acceleration means that velocity will eventually surpass that of C (300 000 km/s), which is impossible and would make all sorts of weird things happen like infinite linear compression and mass. This has been proven in particle accelerators where subatomic particles which weigh trillionths of a pound have been pushed to 97% the speed of light, where they then have a mass of several kilograms!
Also, in order to have a constant acceleration, you need to have a proportionally increasing energy source to cause the acceleration. All the energy in the universe cannot push something past the speed of light, so the earth cannot be experiencing constant acceleration.