The idea behind the checkerboard pattern flickering is that there are two checkerboard patterns with opposite orientations and that they are alternated every frame. Since the pixels don't cover a large enough area, this blends to the eye much better than normal flickering, and if the colors are somewhat close it's pretty much indistinguishable from a single solid color (very useful for making smooth gradients without risking breaking the silhouette).
In theory, it should look like this:
Problem is... the PPU completely breaks this by having every other line shifted by half a pixel. So if you try to apply this trick on the NES, what you get doesn't look anywhere as pleasant (though blurring caused by a low quality signal may sorta hide it):
Ouch, that doesn't look like a checkerboard at all. Generally a better suggestion is to use vertical bars instead of a checkerboard pattern. Unsurprisingly, this actually looks better, though for the record, the outcome ends up being a checkerboard pattern in itself:
And finally, for comparison, checkerboard pattern and vertical bars without any flickering:
There are other issues I'm not taking into account, like any noise introduced by RF or composite encoding. Leaving that for later, I have absolutely no idea how is the noise generated.
