How to make a Cent OS install as similar to an EC2 rhel based instance as possible?

As a one-off, I'd suggest using the AWS VMimport feature, which also allows you to export (some) EC2 virtual machines. More information on that can be found here:

http://aws.amazon.com/ec2/vmimport/

If this turns out not to be feasible for you and if your EC2 instance is EBS-based, you can also try the following:

Stop your EC2 instance, and detach the root volume. Attach the root volume to another running Linux instance at /dev/sdf. In the new instance use the dd command to take a dump of the root partition and output it somewhere you have space (i.e. 'dd if=/dev/sda1 of=/mnt/another_volume/sda1.img bs=1M'). Copy - using scp, ftp or the method of your choice - the new sda1.img to your local machine. You should be able to use this image with Vagrant to spin up a local VM. In the meantime, put your root volume back on your original instance and start the instance again (don't forget to re-attach your elastic IP address if you're using one - they detach on a stop).

Another alternative might be to use 'system-config-kickstart' to generate a kickstart file on your EC2 instance, and use this to build your new local VM. I haven't done this myself though, so you may also want to dump installed packages on your EC2 instance ('rpm -qa --queryformat "%{NAME}\n"') and compare with the resulting kickstart configuration.