How often should "self clean" and "allergen clean" functions be used in an air conditioner?
In lieu of any manufacture recommendations, I would suggest that you use the self-clean method whenever you notice a smell coming from the unit.  As a related tip, if you ever notice the A/C in your car smelling bad, run it on max cool and max fan for 20minutes as this kills most of the mold and bacteria that is causing the smell; my guess is that this 2hour cycle does something similar.

I'm really not sure what the allergen clean might do but maybe run if a couple times a year.

It's probably worth noting that most A/C units don't have these functions and work fine for many years; it might be more of a marketing gimmick than anything else.