Insert a subreddit that you want the images from, and enable the "Show Drive photos and videos in your photo library" option in your Google + settings. Set the folder that you've created as the only BackDrop in your ChromeCast settings and you're done!
If
Any new post in subreddit
This Trigger fires every time there is a new post in the subreddit you specify.
Then
Upload file from URL
This action will download a file at a given URL and add it to Google Drive at the path you specify. NOTE: 100 MB file size limit.
Explore more great ways to automate Google Drive and Reddit