I am not super familiar with the the feedly api (or how it works) but integrating with Algorithmia should be really simple. There is a registration link at the bottom of the blog post and you can check out the docs at http://algorithmia.com/docs.

feel free to drop me a note at diego at algorithmia dot com as well.

Just checked out the docs, looks like they have an easy call to mark one/multiple articles as read - so could have something running periodically filtering out stuff you're not interested in