I found an interesting article here Covering a Replica with Grade A Cotton and Irish Linen (kitplanes.com) about the covering process. I was able to find a place selling Irish linen, albeit at $56 per yard. I've heard (read) that Grade A cotton is still being produced somewhere, and did find a place that carries "airplane cotton", but certainly more research and testing would be needed to determine if it's actually suitable for aircraft use.