I've been struggling with something similar for weeks now. Just figured it out a few minutes ago.
- In mysql workbench, create a new server instance.
- For the remote host address, enter your endpoint address (i.e. xxxxxx.us-east-1.rds.amazonaws.com)
- For connection method, select "Standard TCP/IP over SSH"
- The SSH Hostname is the public DNS of your EC2 instance
- I specified ec2-user (I believe it varies by EC2 Instance type) as the username and then specified the downloaded key file corresponding to the key pair the instance was using.
- The mysql hostname is the endpoint of the RDS instance.
- The username is the username for the RDS instance (i.e. ebroot)
Using that I was able to connect. However, I did not utilize VPC in my setup. Hope this helps. Good luck!