If you followed Bezos/Amazon at all you'd understand.

As to why they can "fly multiple airlines", it's because they contract it out. Pax airlines do the same... some companies even own multipe airlines/certificates and whipsaw them against each other.

It's actually less anti-competitive that amazon contracts out their flying. If they actually owned their own airline that would be more likely to be considered too vertical.

Anti-trust philosophy doesn't really protect labor, it protects the consumers by ensuring they have choices and therefore market forces can keep prices under control. Labor actually would tend to benefit from monopolistic practices... when the company has the lock on the market, labor can demand anything and the company just passes it on to the consumer. Highly regulated monopolies had some of the happiest workers (think ma bell, and pre-deregulation legacy airlines)