What is the effective input resistance on the 6517B electrometer in current mode?

Voltage burden is what is important here. Model 6517B is as close to an ideal ammeter as its voltage burden is extremely low.
However, you can calculate the "effective" input resistance of each range.
20pA range is 20uV / 20pA = 1M ohm
200pA range is 100uV / 200pA = 500k ohm
2nA range is 20uV / 2nA = 10k ohm
20nA range is 20uV / 20nA = 1k ohm
200nA range is 100uV / 200nA = 500 ohm
2uA range is 20uV / 2uA = 10 ohm
20uA range is 20uV / 20uA = 1 ohm
200uA range is 100uV / 200uA = 0.5 ohm
2mA range is 2mV / 2mA = 1 ohm
20mA range is 5mV / 20mA = 0.2 ohms
This is effective input resistance.
The feedback - is the closest you can get to an ideal ammeter.
This means the voltage burden is almost zero. Look in the specs for each range.
So the effective input resistance is just a number. It usually does not matter.