How to add External data source into MySQL?
You cannot do what you're asking (i.e.: replicate content from MySQL to FileMaker). FileMaker doesn't have (as of current version) any way to automatically replicate data from external sources.

Instead of that, you can do something different with equivalent result: access your MySQL data directly from FileMaker. This means FileMaker never has a copy of the data. You just have one data source (MySQL), and have FileMaker SELECT, INSERT, DELETE or UPDATE that MySQL table directly.

You can do that for as many tables on as many MySQL databases as necessary. 

You do this by using in FileMaker an "external data source". Check Connecting to data sources from FileMaker.



NOTE: This has been available in FileMaker since (as far as I can remember) version 12. FileMaker allows also connections to other RDBMS such as Microsoft SQL server and Oracle. Newer versions of FileMaker allows also external sources to be PostgreSQL and others (See here)