This is an interesting idea. You would probably be best having a button pop up when you select text. When you click the button it could have a start discussion popup with the text that was selected already quoted and cited. Then it could post it to the forums through the API. Then it could redirect to the forums with the discussion id given back in the API request. This could be done without extending Flarum.
Perhaps it could check and see if that article already had a discussion created for it and suggest to the user those discussions. This would probably need an extension on Flarum's end for this.
I feel like this could be a cool addition to a news website.