According to Gentleman's Gazette, VBC markets its flannel as "Agnelli flannel." Here's the exact stuff he used to buy:
Agnelli was a great fan of flannel, especially grey flannel. He had all of his suits tailored at A. Caraceni in Milan, but the flannels he used were woven by Vitale Barberis Canonico in Italy. Although he owned various shades of grey, his favorite was definitely the one in the picture. It became so popular that Vitale Barberis Canonico produces it to this day. Although it is a solid fabric, it has many shades of grey with a mottled look that provides the fabric with a sophisticated depth. Overall, every man should own at least one grey flannel suit because it is perfectly suitable for business and casual occasions. On top of that, grey flannel trousers pair with most sport coats and work especially well with blazers.