Best way to implement a scrolling checkerboard background that scales with screen size?

Here is a gif of what I am trying to achieve (this was animated in After Effects).

I have a set of dark and light blue tiles. They should be alternated so that they make a checkerboard, however there are multiple of each type (e.g. dark fireflower, dark blooper) - those are randomly chosen. Any dark tile has an equal chance of being any of the different dark tiles, and same for light tiles. The background is constantly scrolling. I also want the tiles to be rotated diagonally slightly (unlike what is shown in the gif). Also, and this makes it a lot more difficult - I want it to be responsive to different window sizes. Each square should be a constant size, no matter the scale. Increasing the size of the window should add an appropriate number of tiles to the edges of the checkerboard.

It seems like it should be somewhat simple, but I am at a loss as to how it should be implemented. I had an idea involving MoveTowards, but realized it might be choppy due to the way that MoveTowards doesn't move the same speed if it's close enough to its destination.

If anyone has an idea on how to do this, that would be really helpful. Thank you!