You don't appear to have either created a MySqlConnection object or opened it.
But, rather than use a MySqlDataAdapter, I'd see if you can get the value using MySqlCommand.ExecuteScalar:
Dim strSQL as string
Dim objConn As New MySqlConnection(connectionString)
strSQL = "SELECT MAX(memberID) as max_member_id FROM ((SELECT memberID FROM A) UNION (SELECT memberID FROM B))"
Dim command As New MySqlCommand(strSQL, objConn)
command.Connection.Open()
Dim maxMemberId As Integer = CInt(command.ExecuteNonScalar()) ' assuming its an integer
objConn.Close()