Deploying Azure Stack at Amazon AWS
It is not possible to deploy Azure Stack onto Amazon AWS because one of the Requirements is SLAT support which is a form of hardware virtualisation.
The basic premise of Azure Stack is that you have a bunch of Hyper-v servers that emulate the Azure Cloud. The hardware that you use to create the Hyper-v servers needs specific capabilities in the underlying processor (basically to do with how resources are allocated, allowing the hypervisor to give direct access to hardware resources rather than emulating them, which is very processor intensive)
While it is entirely possible to have nested hypervisors (that is a hypervisor running within a hypervisor) AWS intentionally disable the processor capabilities that allow it, so that you cannot run a hypervisor within their EC2 instances. This is a business (and perhaps technical) decision on Amazon's part (and every other cloud operator)