Here the way to download Facebook Friends Email addresses.
The only prerequisite you need is a Yahoo! Mail account.. if you don’t have one sign up for your free account now.
Click on <Allow>,
Click on <Done>,
Your Facebook contacts have successfully been imported to your Yahoo! Mail account.
To export your contacts click on the Contacts tab –> Tools –> Export,
Select an export option.. I would recommend CSV as this format can easily be imported into your email address book,
Enter the CAPTCHA code then click on <Export Now>,
Save this file,
You have just downloaded your Facebook address book.. including all your friend’s email addresses!