Amazon, as the loser, is not happy with missing out on the massive contract. Reports claim that the Amazon Web Services branch head has stated at an internal meeting that the company would be protesting the Microsoft win. The cloud services head allegedly stated that the company would "push" the government to shine a light on what really happened in the bidding process. Reports indicate that Amazon has already filed the paperwork to fight the decision.
Amazon was allegedly seen as the top contender for the lucrative contract, and there is alleged evidence that President Trump got directly involvement in the process. President Trump has publicly criticized Amazon CEO Jeff Bezos, and reportedly stepped into the bidding process and said that "tremendous" complaints were coming from other companies about the contact bidding process.
Allegations were made in a book recently published by former Defense Secretary James Mattis that President Trump had told Mattis "screw Amazon" when talking about the JEDI contract. Amazon is thought to have room based on the claims to argue that the bidding was improper. The goal is presumably to force the entire process to start over again giving Amazon a chance at winning the lucrative contract to upgrade the government's cloud infrastructure.
If Amazon moves forward with a protest, it won't be the first raised in the JEDI process. Oracle lost a legal challenge regarding the contract when it alleged conflicts of interest. Microsoft has had issues with its employees in the past, protesting its involvement in projects for the military. It's unclear at this point if any protests had been raised inside Microsoft over the win.