SQL Backup does not support Amazon RDS. From the information I have read about Amazon RDS is that they provide you with a database instance and they perform all the administrative tasks including backup services for your database instance.
For SQL Backup to operate successfully, you will need to install the SQL Backup Server components which include:
Total of nine Extended Stored Procedures which are created in the master database.
SQL Server Compact Edition, used to cache the backup and restore history from the msdb database.
SQL Backup Agent Service, Windows service that runs the SQL Backup engine.
I suspect that you would be denied installing the SQL Backup Server Components on the Amazon RDS.