This is a follow-up to my post How to Get a YouTube Channel’s RSS Feed. I actually stumbled onto this by accident (by clicking on the red SUBSCRIPTIONS link in the left-hand menu it would seem). You need to go to https://www.youtube.com/subscription_manager on YouTube and at the bottom you will see Export to RSS readers with an Export subscriptions button on the right. After clicking the button it will download a XML file to your system.
Next, if you happen to be using Feedly, you can now import all of your YouTube RSS feeds at once by going to the Organize Sources section which should be at https://feedly.com/i/organize and clicking the Import OPML button on the top-right and selecting the XML file you just downloaded from YouTube. There you go! Other RSS readers should have a similar import mechanism. Hope this helped someone.