Does it make sense to plot the angle in an signal spectrum analyzer?
In this case, the absolute angle you are plotting is relative to the phase at which you are taking samples with your ADC. By the way, it looks like your sample rate isn't very stable, judging from how much the speed of the waveform moving across the display varies.

It would probably be more useful if you were to provide a triggering function for your oscilloscope, so that you get a stable waveform display to begin with, and then display relative phase, perhaps taking the phase of the largest magnitude peak as your "zero" reference angle.

Keep in mind that the phase information in FFT bins that have low magnitude values is mostly the result of low-level noise, and won't be very relevant to the overall signal analysis.