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I am not quite familiar with FileMaker Pro, but based from my research, it's a standalone app? We do not have a direct integration on it.
You can use our web based API to integrate your JotForm account, your forms and submission to your database or system. You can check our API page here: http://api.jotform.com/
If you want to send the submission data of your forms via POST method and fetch it on a PHP script and saved it on your MySQL database, then that is possible. Here's a guide about it: https://www.jotform.com/help/126-How-to-send-Submissions-to-Your-MySQL-Database-Using-PHP
I hope that helps.