Finally, found the exact solution.
If we want to programatically push data into the Contact Form DB, there are two basic things you will need to know:
How to struture your form data so that the plugin knows how to consume it
How to call the plugin’s save data function
Data should be structured like this:
$data = (object) array(
'title' => 'form-name',
'posted_data' => array(
'fname' => $_POST['fname'],
'lname' => $_POST['lname'],
'email' => $_POST['email']);
Where ‘form-name’ is the name of the form, and ‘fname’, ‘lname’, and ’email’ are form fields in this example. Replace them with the fields from your form.
Calling the Plugin
require_once(ABSPATH . 'wp-content/plugins/contact-form-7-to-database-extension/CF7DBPlugin.php');
$plugin = new CF7DBPlugin();
$plugin->saveFormData(&$data);
OR Use CF7's hook
do_action_ref_array( 'wpcf7_before_send_mail', array( &$data) );
The advantage of using CF's hook is that that we do not need to include the CF7DBPlugin.php file, it is a de-coupled approach. The disadvantage is that any other plugin listening to the hook will also get the data.