Backup SQL Server Database on RDS with SQL Server Agent on S3 Bucket

First of all you will need to setup the option group and specify an IAM role which has the correct access to the S3 bucket and keys.

https://docs.aws.amazon.com/AmazonRDS/latest/UserGuide/Appendix.SQLServer.Options.BackupRestore.html

Then your agent will need to execute the SQL command eg:-

exec msdb.dbo.rds_backup_database
	@source_db_name='database_name',
	@s3_arn_to_backup_to='arn:aws:s3:::bucket_name/file_name.extension',
	[@kms_master_key_arn='arn:aws:kms:region:account-id:key/key-id'],	
	[@overwrite_s3_backup_file=0|1],
	[@type='DIFFERENTIAL|FULL'],
	[@number_of_files=n];

You can get away with only specifying the mandatory options only.

https://docs.aws.amazon.com/AmazonRDS/latest/UserGuide/SQLServer.Procedural.Importing.html#SQLServer.Procedural.Importing.Native.Using.Backup