If you ask me it would be easier to dump the access database as an SQL script, change it by hand so it has the syntax that MySQL wants and then import it into MySQL using the command line interface, or your favorite graphical user interface to work with MySQL. Or try to find a tool on the net that can do this conversion for you.
If you desperately want to do it with JDBC, you can connect to the access database using the JDBC-ODBC bridge driver, and to MySQL using the connector/j driver you can find on the mysql database. The rest you do with SQL, select from the access database and insert into the MySQL database. Of course you will first need to create the database and tables in MySQL.