I'd run a sig-gen output (using a single turn only) through the probe using the shortest possible non-coax section, then terminate into a 50 ohm scope input (either built-in or using a 1M input plus a 50R in-line terminator). The terminated scope input gives a 50V/A reference to compare the am503/a6302 output to - even if the sig-gen isn't levelled you'll still get a valid result. Using a few volts of output should give enough signal to test at least the lowest few ranges of the current probe (note that you'll want to test more than one, as there is an amplifier output attenuator switched in/out between the 2mA/div and 5mA/div ranges in addition to the probe input attenuators).
thanks, you solution has been the simplest, I did so. Here are the results:
Yellow voltage, blue current, it looks right

however on the square wave there is this "ripple" overimposed on the static part of the waveform, is it normal ?

with a slower waveform, a noticeable noise is present, however here the current is very low so probably it is normal.

Could be this noise that cause the "ripple" of the second picture ?