Amazon Relational Database Service (Amazon RDS) is a web service that makes it easy to set up, operate, and scale a relational database in the cloud.
With that said, it is not a host that you can ping. In fact many instances of the database product could reside on one virtual machine; the infrastructure behind this is hidden from user.
EC2 security group should work, for EC2 server; are you pinging the EC2 instance correctly? The security rule should be setup as the picture here