I am testing the galvanic corrosion between two metals, following ASTM G71. In this method, a zero resistance ammeter was the material presented to determine the galvanic current measurements. Unfortunately, we don't have access with it. So can I use a digital multimeter instead?
Yes, using Ohm's law: I=V/R.
The only true "zero" resistance ammeter are superconductive. In practical use, the voltage drop across a small resistance is measured. If your DVM can measure down to a millivolt (mV), then a 1 mV drop across a 0.001 ohm resistor shows a flow of 1 ampere current. You'll need to consult the guide (~$45 online) for the maximum permissible voltage drop, and use an appropriate resistance.
Recently, I used the voltage drop across a piece of #16 copper wire to measure currents in the 1 to 5 A range... a switch in the circuit had greater resistance!
Not at all, Zero Resistance Ammeters are dedicated testing equipment provided with internal feedback to automatically compensate for voltage losses caused by the measurement. They actually have "infinite" input resistance, so don't load the source of current in any way, but are backed by an op-amp based circuit which acts like a zero impedance current source. Without a solid theoretical evaluation (impedence matching), you cannot substitute such instrument with a common digital ammeter.