Using vagrant on EC2
So running a virtual machine, on another virtual machine probably isn't the best. But if you want to install Vagrant on Amazon Linux you can do:
wget https://releases.hashicorp.com/vagrant/2.2.4/vagrant_2.2.4_x86_64.rpm
sudo rpm -ivh vagrant_2.2.4_x86_64.rpm
The RPM is the Centos version from the downloads page here: https://www.vagrantup.com/downloads.html
But then you cannot install virtualbox to run a VM. So it doesn't actually work anyways.
Running vagrant inside your AWS box is probably not the right solution. Have you looked into the Vagrant AWS provider?
That will allow you to setup and provision your AWS boxes with Vagrant and Puppet or Chef... if you are using Puppet or Chef to provision your servers then you will have a very portable "scripted" install for your servers that can easily be moved to another provider at a later date...