Did you know that rubber conducts electricity ? Ok it's conductivity is 10^-14 s-m, but if faced with a kragagooogle volt of potential, it will conduct. Carbon fibre conducts rather better... which can be a worry if you are in a sail boat in a thunderstorm.. but to be a useful conductor we are looking for 10^6 s-m or better, better than, or close to copper. What does this stuff do? The article does not relate.
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.