In VB.Net, use ADO.Net to dynamically connect to your MS-Access database. Walk trough the tables and fields using For Each loops. Now send the data to the MySQL database.
The are a couple of ways you can connect to a MySQL database using VB.Net. The first is to use the MySQL Connector class, that is available from Oracle, the owners of MySQL. Read the documentation that comes with it. This can give you a direct connection to your MySQL server. This way you have complete control of your connection and what you do in the MySQL database. Because you have compete control of the connection, you have to manage all aspects of the connection, so you might want something a little more, well, managed.
The other way, which I find a little less elegant, is to create an ODBC connection to the database in Windows and then use the OdbcConnetion class to establish the connecto to the database. See the documentation in VS on Establishing the Connection (ADO.NET).