MySQL DB Migration from on-premises to AWS through replication I am having a production MySQL server with set of 20 databases in on-premises server. Now I require to migrate few databases from production server to AWS RDS without disturbing other databases in one-by-one.

We can perform this activity using AWS DMS. Instead, I am looking at tranditional MySQL replication for setting up replication between existing production server to AWS RDS.

In RDS, as we are not having access to my.cnf, I am not able to set replicate-do-db configuration. Is there any other workaround to setup replication from on-premises to RDS for few databases.
Here's pretty detailed blog post about how to do this:
How to Migrate to MySQL RDS Without Downtime

Our approach was to configure M/M replication between our MySQL instance hosted on EC2 and the new RDS, then gracefully switch traffic from our application servers one at a time without any downtime for our customers.
To clarify, the Non-RDS server in this article refers to MySQL instance running either in your data center or on an Amazon EC2 instance