Simplest way to add a custom icon to a Navbar menu item
You can try to create custom module and implement hook_navbar() - for new items and hook_navbar_alter() - for already created items. In this hooks you can set custom css classes for items and attach you custom css file.

check /navbar/navbar.api.php file.



Looks like links came from navbar_menu_navigation_links(), they already have css class navbar-icon-&lt;item_title&gt;. You create custom css file in you module and add in hook_init(). Example of css styles you can get from navbar/css/navbar.icons.css or even copy it to your file and change if needed or add css for new items.