My impression was flex, or what is being referred to as armour, is not a suitable bonding method. Since the quoted rule 8(a) talks about a metal sheath, and not armour I dont think this applies. The metal sheath could be pyro, or the old alu-sheath cable that had the aluminum sheath. Has anyone out there been able to use flex as the bonding conductor?
In any case, in old houses you never know how secure the lockrings are upstream of where you are working, better to assume it is not properly bonded and install the GFCI as per code.