The sun, gravity, and buoyancy on a flat earth.

The sun:

If the earth were truly flat, the sun should be visible to some extent 24 hours a day, even as a dim light on the horizon.

Using information gathered from as many flat earth "models" as I could find, the sun is usually said to be about 3000 miles above the surface of the earth. And, the diameter of the sun's "orbit" on a flat earth, is somewhere around 7500 miles across. Given this vague information, I've been able to calculate that if you were to stand under the sun's orbit line, and be exactly opposite of where the sun was, you would have to look up 21° above the horizon line to see the sun. This would mean that nothing would be able to physically block the sun's light from reaching you.

The sun has been measured to produce a luminosity of about 3.83×1026 watts, by comparison the Luxor hotels "skybeam" produces merely 1.3 million watts of luminosity. Pilots have been know to see this light from nearly 275 miles away. So how can a source of light 100s of times more powerful be completely blocked by a little bit of atmosphere?

Gravity and buoyancy:

Most flat earthers seem to outright deny the existence of gravity altogether. They claim that objects fall to earth due to their differing density compared to the atmosphere and that buoyancy acts as a force, pulling things to earth.

If this is the case, what dictates an objects direction of fall? If it were only a matter of buoyancy, shouldn't objects move towards an area of the atmosphere with less density than at ground level? If an object were suspended in a pressurized container and then released, would it not simply hover in the center of the container since the atmosphere all around it was equal?

Buoyancy is not a force, but a consequence of one.