Unfortunately veeman8, they are right. Not about flat earth, but about the affect that a constant rate of acceleration would have. For example if you are in an accelerating space craft, such as the space shuttle, the g forces are strongest just after take off, where they are accelerating faster than at any other point in the journey. Once the acceleration tapers off, even though they are still accelerating, the g forces drop off. Once teh acceleration reaches a constant rate (not speed, but accleration ie" increase in speed at a constant rate), the g force will settle down to a stable figure. So for example if the earth were accelerating at a constant 9.8m/s/s we would experience a constant gravitational force. All objects that are in contact with the earth will also be imparted with that force (their momentum). When they are separated from the earth ie thrown in the air, they lose the acceleration imparted by the earth and continue travelling at the speed the Earth was travelling when they separated from the earth. Because the earth continues to accelerate, while the objects continues to travel at a constand speed, the earth eventually captures up with the object.
Wind resistance of course comes into play, but plays the exact same role as it does on a round earth with gravity. The air resistance, the particles of air being pushed infront of the earth, also assist to push the object forward (up) as well, but not fast enough to match the increasing speed of the earth. So therefore in a UA theory as well as in a gravity theory, an object thrown in the air falls back to earth, but it's shape determines to what extent wind resistance slows it's return to earth.
There are many flaws in the UA theory, but this issue of falling objects is actually one of the, actually the only, elegant facets of the UA theory.