Q:

Penumbra colors of a flat earth's sun-shades

So, I have been watching a lot of flat-earth debunking videos on YouTube, which has tickled my world-building bone. So, I'm imagining a world with a sphere of sunlight-level luminosity hanging relatively low above a flat disc, square or plane with a number of large opaque objects orbiting it to create a rather complicated day-night cycle.
What I'm wondering is, just how much atmospheric scattering would there be around these sun-shades, and how much variance could be achieved in the penumbra coloration by varying the size, shape and/or orbital radius of the sun-shades?
Here's a mock-up of the situation I'm talking about, superimposed on the emblem of the United Nations:

In this image, the yellow star represents the sun, the red rectangle represents a sun-shade, and black represents the full shadow cast by the shade (i.e. that's where it's night). The area in orange is the approximate area of the penumbra, i.e. where the light scattering around the edges of the shade falls. What I'm wondering is, what colors can the combination of atmospheric scattering, diffraction and/or reflections from other (not pictured) sun shades produce?

A:

Blocking sunlight does not cause scattering or change the observed colors in the way that a sunset does; it only makes the sky darker or lighter, depending on how much sunlight was blocked. With all of the sunlight blocked (the umbra), we have night or near-night. With none of the sunlight blocked (the antumbra), we have sky blue (not including sunsets). And with a partial amount of sunlight blocked (the penumbra), we would just have something that's between sky blue and dark blue or black, like shown in the following image:

Changing the shape would not have any spectacular effect on the coloration of the shadows as you've described, but it would have a very interesting effect on shadows cast by the partially eclipsed sun. Below, you can see the effects on shadows during a real-life solar eclipse:

As you can see, the shadows have the same crescent shape as the eclipse itself. In your world, these shapes would vary as much as you would like them to, depending upon whatever shapes and sizes you choose for your sun shades.
You have stated in your question that the sun shades were opaque. However, if you wanted to have the shades partially opaque, that would allow you to change the amount of blocked sunlight without needing to change the size and shape of each sun shade.
If you really want there to be different colors, you could have some semi-opaque, colored shades that actually change the observed colors in whatever way you want them to. 

Or you could combine the varying levels of brightness due to the sun shades with the different colors available during a sunset:

