In regards to the burden of proof: it's been a few hundred years now that the entire scientific community has known gravity to be an observable force, easily proven with countless experiments (as demonstrated on this very forum like a billion times). Your universal acceleration idea is laughable - if it were true, the Earth would be moving many many times faster than light by now, which is obviously impossible. All flerfers can do is inaptly pick at various basic science ideas they don't understand -- there is no actual evidence for your claims, and no experiments to prove them. So, nice try, but the burden of proof is still on you guys.
Ah, so not only do you not understand how the burden of proof works, you also don't understand acceleration or Special Relativity. Excellent to know, as it reinforces that you haven't read the wiki or FAQ (hint: we would not be moving faster than the speed of light). I'd suggest you look in the mirror before accusing people of inaptly picking at various basic science ideas they don't understand.
For once, I have to agree with the FE'ers here.
Einsteins' general relativity says that there is NO DIFFERENCE between a uniform acceleration and a uniform gravitational field. No possible experiment can distinguish between them.
Since the gravitational field of the Round Earth is basically uniform (at least for day-to-day experiences) - it could indeed be replaced by a uniform acceleration - and you would not be able to tell the difference.
The issue of the Earth speeding up until it's going faster than lightspeed is also not a problem. Einstein's special relativity tells us that you can't meaningfully measure speed except as speed RELATIVE to something else. Since the FE'ers claim that the Earth, the sun, moon, stars, planets...EVERYTHING is accelerating at the same rate - there is nothing left in the universe to measure the Earth's speed relative to. So even asking what it's speed is would be a meaningless question.
So - those two SIMPLE problems don't debunk the Flat Earths' "Universal acceleration" claim.
But - as usual with FEism, you can look a little deeper and find the flaws in it.
SO: I said before that Earth's gravitational field is only approximately uniform. But gravity varies with altitude (less at mountain tops, more in deep valleys) - it varies at the poles (more) and equator (less) - and it even varies a tiny bit according to the types of rocks under your feet.
Universal Acceleration can only simulate a uniform gravitational field. So if things worked the way they say, we wouldn't get all of these variations in gravity - it would have the same, exact value everywhere.
They try to 'fix' this problem (I'd prefer the word "botch") by claiming various things - such as that the sun and moon (and perhaps also the stars) do indeed have true, 'for real' gravity. This is needed (for example) to explain how there can be tides caused by the Moon's gravity.
But why there would be changes in gravity at the poles and the equator is not well described.