I live in the U.S. desert Southwest where we wear light-colored cottons in the summer and dark-colored cottons in the winter. Someone recently gave me some luscious cranberry cashmere that would be perfect with black braid and silver buttons. I might use it for my Chanel jacket project, but I'd probably only be able to wear it once a year when I'm at a conference in the Midwest or Northeast. And handling wool in August and September isn't my idea of fun.
A few searches have yielded a couple of possibilities. A "creamy organic cotton boucle" at http://www.casualelegancefabric.com/products/creamy-organic-cotton-boucle.1245.html and a cotton double-knit fabric in off-white or black http://www.trimfabric.com/double-knit.html . Chanel used a lot of jersey, but I've never seen an actual example so I don't know what underlining fabric was used and how it affected the drape.
A linen/cotton or linen/rayon blend might also be good. It seems to me that the jacket works because it is soft in spite of its boxy shape. Any fabric suggestions, especially regarding cotton, linen, or silk, will be gratefully received!