There is no such standard functionality on the site. You would need a server side implementation that responds to the Feeds bots requests and produce an RSS feed from the Hot Network Questions list.
I've created an app in Glitch here (and find the implementation here)
The Glitch app offers a route
/hnq/:site. This route returns an XML RSS Feed. The feed can then be read by the Stack Exchange Feeds bot. The bot will then post new items in the chatroom.
:site parameter can be
- a single domain name of a site
- an exact domain name match of a site, indicated by a = as prefix
- a list of domains to include, indicated by a + as prefix
- a list of domains to exclude, indicated by a - as prefix
- a combination of domains to match, include and exclude
Examples of each option are
Here is an image showing how you can configure a feed in your room:
And you can see the result of the RSS items being posted here.
Additionally there are RSS feeds for migrated questions, basically offering an implementation for Make migrated questions eligible for First Posts review
The app also offers an interactive Chart to see all the hot questions, their score and answers plotted over time.