Best way to pg_dump PostgreSQL on RDS to S3
You can directly upload the (gzipped) pg_dump results to s3 using the aws cli:

pg_dump -Z 9 -v -h ${DATABASE_HOST} -U ${DATABASE_USER} -d ${DATABASE_NAME} | aws s3 cp --storage-class STANDARD_IA --sse aws:kms - s3://my-bucket/dump.sql.gz


At work we wrapped this in a script which additionally fetches the required credentials from parameter store and then stores the backup in s3. The script runs within a docker container as a scheduled ecs task. Maybe the code in this repository will help you.