This summary doesn't give numbers, but the journal article being discussed does. About 3e3 to 1e4 S/m for different preparations, compared with zero for untreat

This summary doesn't give numbers, but the journal article being discussed does. About 3e3 to 1e4 S/m for different preparations, compared with zero for untreated silk. Performed as a two-probe DC measurement, so once you factor in contact resistance it might be even better. The details are scarce, so you'd probably want to see it repeated more carefully before concluding anything.