Here are a couple of images I was given by an Aerospace Engineer recently. I don't know if he was trolling me or not, so I provide them without further comment.
If you zoom in close enough, the horizon looks flat. (Alternatively, the plane is not high enough for the earth to look round with that focal length)
The second one:
All that matters is that Mercury isn't in the line between the Sun and the Earth. Take a look here [0] to see that there are times when Mercury's orbit would be visible from Earth.
Even then, I'm not sure why the Earth being flat would have anything to do with Mercury's visibility, since it would still be visible even if the Earth were flat.
[0] http://jwilson.coe.uga.edu/EMAT6680Fa09/Yoon/EMAT%206690/Fir...
They're trying to imply that a spherical Earth would prevent a visible Mercury at night. It's still nonsense.
It's proposing the idea that you can't see anything in a mirror that is facing around the corner from you. Venus is reflecting the Sun's light to you on the night-side of Earth, just like a mirror reflects an image to you even though you can't physically see around a corner.
Think of it as Venus orbiting inside Earth's orbit, but not directly between the Earth and the Sun at the time you can see Venus.
This explains it better than I can: https://www.quora.com/How-is-Venus-visible-in-the-night-sky-...