Hi @Marketingguy,
As far as I know, and that you found, Klaviyo doesn’t sync its List (or Segments) to Mailchimp - you would have to export it from Klaviyo and import it into Mailchimp.
However, I’m not sure if this will work for you, or what specific part of the Mailchimp Facebook Audience you need , but Klaviyo can also sync your List directly to Facebook as a custom audience. In fact, any List or Segment can be synced to Facebook - so if that is your goal, you may not have to rely on Mailchimp to do this.
Check out this documentation on how to set this up:
Hope this helps!