Why does my Arduino 3.3v fluctuate?
Arduino output voltages may "fluctuate" a few mV but what you showing us in that gif is really unstable.

What you should be doing is:


Disconnect everything from Arduino except the power source
measure the voltage again;


Is it stable? the problem was because of pulling too much current that causing voltage drop and instability .

Is it unstable?


Try checking with another MM and/or change auto-range to manual.


Is it stable when measuring the voltage with another MM? something was wrong with your previous MM.

Still unstable?


Connect the Arduino to a 9V power adapter and disconnect the USB cable.


Measure the voltage again, if it's stable the problem was because of some error in the cable or USB power source.

Voltage is still unstable?


change the 3.3V voltage regulator.


It should fix the problem if not report back to do some more in-depth problem solving.