Amazon prime air is not going to fail.
They just need to be able to move cargo for less cost than with UPS. That's all it takes for this thing to be successful for them. Even if they are paying more than they pay UPS, they are using these planes for marketing so may not even care.
The idea that UPS is flying a plane load of amazon boxes for less than amazon is paying someone like ABX? No chance. A UPS pilot is probably getting 50% more than the ABX guy flying the exact same plane. With better work rules, better guarantee etc.
Yes, individual carriers might have trouble with staffing in general. But amazon will move the flying around to where folks are able to staff or raise wages. Good news, if they do expand more (big IF) they may need to pay more or move flying to airlines that do.