So for this method you will in fact need a yahoo email address.
Note: when creating an account you will need to confirm your account via a mobile device. Once you have created your account: login.
Step #2: Preparing to pull emails.
Now navigate up to the top where it says "Mail", with a purple envelope next to it. Click it, and it should take you to your inbox. Once in your inbox, go to the top left and hit the "contacts" tab.
Step #3: Getting the emails
As you proceed to do this, a Facebook pop-up will appear; asking you to login. Obviously you login. And wallah! All of your friends on your Facebook friends list will appear in your contacts. And the email they use to login will be displayed right under their name.