According to a Bloomberg report, Amazon is testing it's own "Amazon branded delivery service" to compete against FED EX and UPS.
The service is called "Seller Flex" and is being tested on the West Coast.
Amazon is one of UPS largest customers and represents about 10% of it's traffic. This would certainly be major competition for FedEx and UPS. Amazon usually uses these carriers in the final few miles for delivery of packages. Amazon is looking for ways to decrease costs perhaps and also gain an additional revenue stream.
Shipping is never "free" like Amazon offers with Prime ...it's buried in the total costs of the business and used as a competitive weapon for online business.