It's not just possible, it's already in the works.
Back in March Amazon announced plans to lease 20 Boeing 767s. Their first plane flew at an airfair in Seattle a few months ago. Recently they've been showing off their long-haul Prime semitrucks around Seattle.
Factor in Amazon Logistics (last-mile Fedex/ups/usps alternative) and Amazon Fresh (last-mile food delivery)... it's happening. I think we can expect big plays in 2017.
* they also have their drone thing... I think that's just a moonshot hype project.
At its core Amazon has always been a logistics company. They already put warehouses close to airports so it's not much of a stretch to take over the air freight. Last mile is another issue, UPS, USPS, FedEx and the rest will continue doing that for a long time.