You can average samples of each channel together (sum to mono). The catch is that there will be phase cancellation which may or may not be a problem for your analyzer. If the source audio for instance has a Haas effect applied the spectrum will show comb filtering that doesn’t really exist.
You can also show the difference of the two channels (convert to a “side” channel). It’s interesting from a data analysis perspective but not perfect for the user to see anything intelligible.
An alternative to both is to recognize that the perceived spectrum is going to be affected by masking, in other words the stronger signal will be more apparent. A very naïve way to deal with this is to take the FFT of both channels, and plot the bin of whichever channel has the highest magnitude.
The flaw there is assuming that both channels are correlated. You can always just plot two lines, or have two plots.
If the goal is a simple analyzer that tells the user in general what’s going on, using a mono sum or plotting the channel with the highest bin is probably the best. If you want a super accurate display, having separate channels is a good option.