I know, that the original question is from last year, but maybe someone else wants to do something similar.
csf I'm wondering if it's possible to use the badge icons inline somehow, in a way easier than creating an image and linking to the image?
Looking at the linked page address of your forum (/p/2-user-groups), I assume, that you can make use of HTML (sijad's flarum-ext-pages extension). If that's the case, you can go along the lines of:
<sup><span title="Rocket" class="Badge" style="background: #cc3300"><i class=" fa fa-rocket"></i></span></sup>
This will show a little white rocket in a red circle with a slight shadow according to flarum's badge style.