The Associate level AWS courses typically devote a single slide to this topic. The Advanced Architecting on AWS course goes into more detail. However, there is no lab on the subject.
qwilab.com have a lab “Introduction to AWS Database Migration Service” which costs 1 credit ($1).
The lab provides a basic understanding of the DMS service, and will be useful if you have never used the service before, and even if you do not have a background in installing and using SQL databases. The lab template builds an EC2 instance with the MySQL installer already downloaded.
The lab guides you through installing MySQL Server and MySQL Workbench, creating a database, populating it with some provided data, and executing a test query. The MySQL database will be the source database for migration. This database could equally be a database in the data center, and the process would be the same.
The lab template builds an Aurora database to be used as the target database.
The lab guides you through creating a DMS replication instance, source and target endpoints, and a DMS task which migrates the data.
To validate the migration, you connect MySQL Workbench to Aurora and execute a query.