How to use the oscilloscope to show the average of the DC current?
When you zoom out, you are getting aliasing.  Even if you didn't get aliasing, you'd get a fat horizontal line that wouldn't tell you where within the fatness the average is.

What you need to do is low pass filter the signal before presenting it to the scope.  A simple resistor and capacitor should be good enough.  10 k&Omega; in series and 100 nF across the scope probe will attenuate the 20 kHz ripple to oblivion for your purpose.

Some scopes have measurement features that can do things like calculate the RMS from all the samples.  That may sound simple, but can be tricky too.  You have to make sure you have enough cycles on the screen or in the sample buffer (not necessarily the same thing) to get a good average and not have partial cycle artifacts, but not zoomed back so far that you get aliasing.