This app was mentioned in 2 comments, with an average of 2.00 upvotes
With dashboard cast on android you can throw an RSS feed to the big screen, but it's just titles.
~~Your best bet is just to cast your phone display or chrome tab for this one~~
Apparently one exists - https://play.google.com/store/apps/details?id=com.wearhub.reddithub
But it only cast pictures and videos
Try cast for Reddit
https://play.google.com/store/apps/details?id=com.wearhub.reddithub
Its not a full Reddit client, it just take the media and cast it on Chromecast, works just fine