Early war CSA flags were indeed almost all silk as there was an ample silk supply in the South before the war. The blockade took care of that as it was not considered a war essential. Silk was also the traditional material for making military flags.
By early 1862 almost all CSA flags were wool bunting which was imported entirely from Britain. The wool was tougher and for modern conservation purposes, lasts a lot longer than the silk flags did. Since wool bunting was considered a war commodity it got placement on the blockade runners.