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...I would like to know what would be the least reflective fabric I can use for this project. I'm not sure if cotton, polyester or some other type of fabric would be the least reflective.
In my experience, cotton is usually less reflective, although a poly-cotton blend can be almost as good.
One common and reasonably-priced option is to use flat bed sheets from Walmart, Target, etc. You can get different sizes depending on your needs, and they're already hemmed so there's no risk of fraying in use or with laundering.
Unless you can shoot with enough background-subject distance to blur the BG, be sure to iron them or steam them before use, and roll them rather than fold them for transport.