Backup RDS to S3

exec msdb.dbo.rds_backup_database
        @source_db_name='database_name', @s3_arn_to_backup_to='arn:aws:s3:::bucket_name/file_name_and_extension',
        @overwrite_S3_backup_file=1;

Restore from S3

exec msdb.dbo.rds_restore_database
          @restore_db_name='database_name',
          @s3_arn_to_restore_from='arn:aws:s3:::bucket_name/file_name_and_extension';

Check RDS Status

exec msdb.dbo.rds_task_status @db_name='database_name'