Does Feedly work offline?
Feedly does not have an offline mode at this time.
Some apps that run on the Feedly backend and API do offer offline reading. Reeder is a very popular option on iOS. The full list of partner apps can be found here: http://www.feedly.com/apps.html.
Another way to read offline is to use Pocket (getpocket.com). With this, you can save articles from Feedly to your iOS or Android devices for offline reading. Pocket syncs offline, so whenever you are without a connection, you can use Pocket. It's not the most seamless experience but it is a possibility for offline reading and syncing. You can learn more about saving from Feedly to Pocket here.