In Inoreader, make available your feed of favorites, then use that URL into DT to sync that RSS. You can then use a custom CSS style into DT. Once you want an article, favorite it and sync DT feed.
It is in the specific Inoreader documentation, but I cannot find now where it is. You can create a custom button that will share the current selected item, passing those parameters in the URL.
Theoretically, one could directly connect Inoreader with DT using that URL, the exported user feed (that exports parts of Inoreader content, like your manually added websites, your Favorites or even your entire feed as an ATOM/RSS/JSON/HTML), but you have to “mess” with a custom DT CSS file, because Inoreader has its own styles you must replicate if you want so see similar stuff.
For example, in my case, and inside Inoreader only, I have this custom CSS got from looking inside the Inoreader HTML generated code: