Can you average out focal length from different camera calibration sessions?
No, it is not a good idea.  Typically, you want to limit the volume of space relative to the camera in which you want to do your measurements, and you want to use a single calibration target appropriate for that volume.  In theory, you can calibrate with any number of different patterns.  In practice, however, most implementations assume that the pattern is the same in all calibration images.

In any case, if you insist on using multiple patterns, you still want to jointly optimize the parameters, not just to average them after the fact.  And you would most likely have to implement that yourself.