No there is no reactive driver for MySQl. There is one for Postgres:
https://github.com/r2dbc/r2dbc-client
it uses all the reactive bits from project rector (collections are return as flux). Of Course you are back to working with prepared statements. And pulling data directly from the Serch reasult.
And the one for the oracle DB:
https://github.com/oracle/oracle-db-examples/tree/master/java/AoJ
But it uses a blocking JDBC calls and only hides the problem of behind thread pool. However it represent the current effort at Oracle to attack the problem. And it is not a trivial thing as there is a certain philosophy when working with relational databases of consistent state. That is why your query result is return all at once unlike mongodb that can return result as it comes in.
Because of that any ORM (hibernate, eclipselink) tooling is nowhere.
I think for production code we are stuck with blocking calls for now.