That looks like a real fun tablecloth.
A Churn Dash block would allow you to incorporate you red and block in the border around your chickens. It's also known as Hole In The Barn Door, so this would be like the chickens peeping out the barn door!
Kind of like them being in a cage!
Another idea would be to keep it simple and alternate your chickens with the red and black. However, you did not mention how much you have, so hard to know if you would be able to do that.
The white could be used as a sashing as you suggested. However, for me, for a table cloth I would not as the white would show any stains long before the other fabrics/colours would.
Something else to consider when doing your piecing and final placement in the tablecloth, would be the direction the chickens are facing. It'd be nice to have them facing each person as they sit at the table!