You can manually update font-awesome icons.
1. Go to font-awesome
2. You can find Downlaod font awesome free button, get the download.
3. Use your child theme to create a css directory as in parent theme and add fontawesome.min.css file from the downloaded package inside it.
4. Now you need to enqueue it from your child theme; open functions.php file inside flat-responsive child theme
5. For instance; Take reference from the function as follows;