I have added the Font Awesome script and it is being loaded in the source code also. But the icons are not being displayed in the post editor. Any possible solution?

1
Make sure you’ve registered the stylesheet for the editor:
add_editor_style( 'http://maxcdn.bootstrapcdn.com/font-awesome/4.3.0/css/font-awesome.min.css' );
This should be in your functions.php
https://codex.wordpress.org/Editor_Style