The current feedly apps (iOS and Android) do not offer offline article caching.
This is a feature we are looking into.
If you’re looking for offline support, some feedly partner apps support it (eg.Reeder and Newsify on iOS, or Press on Android).
Those apps are powered by the feedly Cloud API and will seamlessly recreate your reading environment (all your feeds are sync’ed from feedly when you login).
To explore the feedly partner apps and their features, visit http://www.feedly.com/apps.htmlVvonHistria commented
I am really curious about this. It is the most desirable feature, yet Feedly refers us to a competitor. I think it would be really really useful if Feedly would explain why it doesn't plan to develop this option.