That helps narrow things down. The error you're seeing means that your server doesn't the root certificates that can verify Amazon's identity. I'd recommend contacting your hosting provider to get the updated root certificates installed to be able to verify the identity of
api.amazon.com
As an interim solution, we have the option of "Disable SSL Verification" in JFBConnect which will skip the check. It reduces security slightly as the communications can't be verified to the social networks. All data is still encrypted and should be very secure though.
I hope that helps, but please let me know how it goes or if you need more help.
Thanks,
Alex