More likely that Amazon will come out with its own currency.
They can try, but I don't see why people would adopt it.
Reason #1
Because it's fricking Amazon.
So people will buy into amazon's currency so they can spend it on Amazon? Might as well just vouchers. And any company can create their own money, but it wont be cryptocurrency.
If they did would it be 100% pre-mined?
Doubtful.
They'd probably "mine" it by offering rewards programs to get it into circulation. But it can only be spent on Amazon, issued by Amazon, etc. and might offer some value that cash doesn't, like "X amount off orders worth $Y" or expedited shipping, reduced sales tax, whatever.
Amazon likes to handle things in-house... they're the largest shipping operation in the history of humankind. Tens of thousands of outlets and warehouses. A whole internal system.