The surface tension of air?
It holds strong over nothing larger than the tip of a hypodermic needle. It will not hold the air in as the Earth accelerates.
If it is constantly accelerating, how is the air not being compacted to the point of combustion, or flowing over the edge of the flat earth and floating off into the void of space?
It doesn't flow off the edge of the Earth because there is a gigantic wall of ice and rock at the edge. It isn't being compacted to the point of combustion because the acceleration isn't high enough to raise it to that kind of pressure, far short of it in fact. If the Earth accelerating at 9.8m/s/s through space could compress air to the point of combustion, so could a stationary Earth with a gravitational constant of 9.8m/s/s. Remember, the effects of a constant acceleration and a gravitational field are locally indistinguishable according to relativity.
Not true. In a flat earth, because of that lack of an actual gravity to
hold air to the earth, pressure cannot be readily relieved other than by having the air flow over the sides. However, this would not be entirely possible, because air would become trapped. Sheer inertia and acceleration would cause it to act like the compression phase of a turbojet engine and would combust the air.
In a round earth, with gravity, the air around it is held in so that none escapes, at it, through this acts like a closed system, and pressure is relieved throughout.