There is only a way to connect Kalipso to a MySQL database, is by installing an ODBC Driver to do that. Links to download below.
Just download the connector and install it.
After installing and rebooting the pc, create a new ODBC of 32bits (System DSN) using the installed connector.
After creating the connection as test it successfully you just need to add this connection in Kalipso a use it as a normal database. Keep in mind that MySQL the queries are a bit diferent and does not support all the functions as an SQL Server connection.