Custom function doesn't get triggered by hook_cron()
Can you change:

function _my_custom_function() {
    // Define fields
    $fields  = array('field1', 'field2', 'field3');
    // Trigger Batch for import
    batch_set(_start_my_batch('myfile', 'mytable', $fields));
}


Into

function _my_custom_function() {
    // Define fields
    $fields  = array('field1', 'field2', 'field3');
    $function = '_start_my_batch';
    $batch = $function('myfile', 'mytable', $fields);
    // Trigger Batch for import
    batch_set($batch);
}


I think you should check every functions separately (hook_cron, batch function..) and make sure they work. After that put on the same place and play. The Example Module also is the very good place for doing this kind of stuff.