In the header settings, Razor enables you to set the area to the right in the navigation bar to any sidebar content. (By default this area is set to the search box.)
So first you need to create a new sidebar area (Appearance > Sidebars) and then add your content (i.e. your HTML that displays your flag icons) to that sidebar area (Appearance > Widgets), and lastly you need to edit the headers you are using (Appearance > Layouts) so that the Main Menu – Right. option is referencing the new sidebar you created.
The Razor theme does not include any flag icons, you’ll need to provide those yourself, as well as the actual HTML content that displays those icons and links them to the appropriate pages.