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I'm not sure if I have understand your question correctly. You want to retrieve the emails from your database and make it the form recipients? If so, that's possible either using Jotform API and write your custom script. Or, this method which I think a bit easier.
Visit http://instant.jotform.com, pick a form and enter the email address you want to be the form recipient. You can add multiple emails separated by comma. Example:
You can add up to 10 emails as the maximum limit. You can then write PHP script that fetches the email data from your database and print it on the link.
http://instant.jotform.com/contact-us/<?php echo $email; ?>
If you have further questions, let us know.
Have a good one!