Measuring a smartphone's power consumption
In normal conditions i.e your phone is in standby mode and your screen is locked,  then as you said the once the phone is charged, the current consumed by the charger is 0.

Now when you unlock your device(but still the charger is connected) and start to do some operations(e.g. playing games or watching video), then the phone will start to consume power from its battery. At this instant your phone has drained its battery to a small percentage. But the phone won't display since its a small drop. In parallel your phone will try to charge the phone since the battery has drained. 

This causes the current to be drawn from the charger. As per the operation you do on the phone, the battery will get drained soon and the charger will try to charge the battery as soon as possible by providing more current. This causes a variable current change on a charged phone.