I hate SPAM with a vengeance but I do LOVE getting really relevant emails that offer me new techy stuff for FREE!
And today I had an email from GetEmail.io which promised that I would be able to gather email addresses from Linkedin addon in minutes and all for FREE. I had to try it and I am glad I did as it works really well.
Just add the extension to Chrome, go to Linkedin and find the person whose email you want and BOOM! there it is. Sure, it does not work 100% of the time and especially for contacts/companies in China or Russia, but then its very new and I would not expect it to be perfect.
So try it, you really have nothing to lose!