If you’re referring to the paper USD is printed on, it’s cotton rather than paper.
But even if there was a shortage, I doubt that on a country level USD (or any currency, for that matter) is bought in physical form - it’s just credited to the country’s bank account.
Linen comes from the flax plant and cotton comes from the cotton plant.
Linen versus cotton have a great history. Linen was used on WW1 era airplanes as outer skins because it didn’t run like cotton canvas when the material was shot through.
But even if there was a shortage, I doubt that on a country level USD (or any currency, for that matter) is bought in physical form - it’s just credited to the country’s bank account.