I would advise that you first insulate the application against this change by making all the app services interact with the backend using a Repository pattern. i.e. put the repository abstraction in place that will allow you to then switch the DB internally. I also like to follow the expand-contract-expand pattern for consumers explained in http://martinfowler.com/
articles/evodb.html for existing data.
When you refactor your application to use MySQL leverage something like Flyway or jOOQ to manage future DB migrations.
At a raw DB2 data and schema level there are tools like DBConvert that can be used to move and sync the data.
So its a combination of both app and data patterns along with some Blue/Green routing magic that will be needed to move the data from DB2 to MySQL.