Please explain what you mean.
Okay, so here's how relativity works.
Suppose Alice and Bob are flying along in two different spaceships, ship A and ship B. Suppose they're flying in the same direction, and that Bob's ship is going v meters per second faster than Alice's.
Alice's ship and Bob's ship are called "reference frames". They're basically places you can take measurements from. Two reference frames are the same if they're moving in the same direction at the same speed. Alice and Bob are moving different speeds, so they're in difference reference frames. Einstein's relativity assumes that in two different reference frames, people will measure the same thing differently, except the speed of light. That is, all measurements except the speed of light are "relative the the observer." Everybody, no matter how fast they're moving, measures the speed of light as being a certain constant "c". Everything else, however, will appear different in different frames.
But, within a given reference frame, where everything is moving the same velocity, relativity has *no* effect. Since velocity is relative, the only time you see the effects (time slowing down, objects getting shorter) is when you observe something that's moving faster or slower than you.
On the Flat Earth, everything is moving "upward" at the same speed as the Earth. So, from the perspective of people on the flat Earth, there are no relativistic effects. Somebody outside, in a spaceship watching the Earth whizz by, will see the effects: the Earth will get even flatter, time on the Earth will slow down, and its mass will increase, though of course the speed of light on the Earth will always be the same to him.
From the perspective of people on the Earth, everything that happens on the Earth will appear normal. They also will not notice that the Earth's (or their own) mass has increased. However, they will notice relativistic effects of length contraction, time dilation, and mass increase on the spaceship.
This idea of the mass increasing is an important one, because the amount of force required to move an object changes based on its mass (F=ma). On the Earth, like I said, you do not notice this change, so you have to apply the same force to, say, lift a 1 kg box no matter how fast the Earth is moving. From an outside perspective, however, it will appear either that accelerations ("a") decrease, or forces ("F") increase.
So assuming that the Earth is propelled upwards by a constant force, an outside observer will see that the flat Earth's upward acceleration decreases over time. We will not notice this; it will always appear to us that the Earth is accelerating upwards at 1g. Once the Earth is moving the speed of light (relative to, say, Bob), it will appear to Bob that it is not accelerating at all (but it will appear to us that it is accelerating at 1g).
So that's what relativity means. If you're still not sure what a reference frame is, let me know. The important thing is that inside a reference frame, everything is "normal". It's only when you compare two different reference frames that you start to see the effects of relativity. It's also important to understand that the speed of light is not a brick wall that makes you suddenly stop accelerating; it's just that people in other reference frames see your acceleration always decreasing as you go faster and faster.
Anyway, hope this helps. If you're still fuzzy on it, let me know about which part in particular I can be more clear.
-Erasmus