Measure current across shunt resistor (Power Analysis)
In the graphs they've got 2.5mA tops, so you've got about 2mV on that 1.2R shunt resistor.

And Uno's default ADC reference is 5V divided into 1024 steps each of them roughly 5mV. That's more than peak value of measured voltage.

And with such small sampling frequency you won't be even able to spot fast changes as you'll be measuring much slower that it needs to be.

ADC step precision can be better by using internal 1V1 reference, but it's still way too big step. And there is no other option on UNO. The Mega on the other side has also possibility to configure diferential ADC inputs and with 1x, 20x or 200x gain. But it's not supported by Arduino core, so you'll have to do it directly. However it won't help much if it's sampling too slow.