In a flat earth, far distant objects would only disappear due to mist and other atmospheric effects - and because perspective would eventually hide distant mountains behind relatively small bumps in the ground that were closer to you.
On a calm day at sea - if the world (and therefore, the ocean) is flat - you should be able to see as far as the atmospheric clarity allows…which is usually at least 25 to 30 miles on a clear day.
So on a flat earth, the distance at which objects would become impossible to see would only be limited by atmospheric clarity - and the distance you could see wouldn’t vary with how high you are above the ground.
Let’s take a concrete example:
As a kid, I lived near the town of Dover, on the south east coast of England - at a point on the English Channel that is closest to France.
Dover is the site of the famous “White Cliffs of Dover” - and equally famously, from the top of the cliffs, on a clear day, you can see all the way across the English Channel to the coast of France - which is 20.7 miles away. This is well known to be the only place in mainland UK from which you can see “Foreign Soil” - and the White Cliffs are famous for that exact reason.
However, if you stand at the base of the cliffs - you can’t see France, no matter how clear the air is - and no matter whether you employ binoculars or even a telescope. If you could, then you'd be able to see France from St.Margret's bay - which is a little closer to France and has a broad sandy beach. But you can't.
If the world was flat, then on a clear day, it wouldn’t matter whether you were standing at the base of the cliffs or on top of them - you’d be able to see just as far either way. So this is a good demonstration that the Earth is indeed curved.
We can even crunch the math (or cheat and use the online: Distance to the Horizon Calculator) to verify the plausibility of this claim.
If you’re standing at sea level (on a beach, at the bottom of a cliff, for example) - then with your eyes being about 5 to 6 feet above sea level - the horizon is a mere 2.7 to 3.0 miles away. The white cliffs are around 350 feet tall. If you stand on top of a 350 foot cliff (and assuming you’re 5 to 6′ tall), then the horizon calculates out to be is 23.1 miles away…which explains why you can see the 20.7 miles across the channel to France…when the air is clear enough…but ONLY from the tops of the cliffs.
QED.