Flarum uses the TextFormatter library for formatting user content, and that library comes with a plugin called MediaEmbed https://s9etextformatter.readthedocs.io/Plugins/MediaEmbed/Synopsis/
MediaEmbed has a series of template for popular websites that can be embedded. You can see which sites are included at https://s9etextformatter.readthedocs.io/Plugins/MediaEmbed/Sites/
If you would like to implement a new site just for your forum, you can take a look at the instruction in their docs https://s9etextformatter.readthedocs.io/Plugins/MediaEmbed/Add_custom/ and you should be able to find somewhere on this forum examples of how you can add this code to Flarum's extend.php.
If you would like to add a new site to be supported by all Flarum installations, including FreeFlarum (which I am assuming you are referring to), then you would have to submit a proposal directly to TextFormatter. The update might not become available before Flarum 2.0 because I believe Flarum is currently on an older TextFormatter version.
You could also package the additional templates as a new standalone Flarum extension.
If you already did all that and are encountering errors inside of the embedded iframe, take a look at your CSP policy, cookie policies, iframe sandbox attributes, etc. Browsers are very sensitive about what you can embed into what these days. If you are not hosting the forum yourself, you might not be able to make the necessary changes to allow the iframe to load properly.
