It would appear they are doing some server side magic to determine which stuff shows up (hence the need for their own server):
"...Well, it has a set of algorithms that are looking for highly engaged items. You know, items that have lots of comments, likes, or retweets. It also has an algorithm that senses photography that’s been linked to from Facebook status messages and it lays those photos out."
I finally got the facebook part to work and they ask for every privilege you could imagine, including "access your info when you are not using the app". Too bad.
A friend of mine did something kinda similar. They might be somehow scraping/processing the twitter/facebook links. Ends up being pretty processor intensive.
Ehm, wtf? Why does it even need a Flipboard server? What happens to my twitter account info? All they need is a XAuth token, right?