Where does one obtain licensing for the product? Crazy place to have to ask this question. But no one seems to know. The name went from LiveCycle Forms Designer to AEM Forms Designer. Maybe that's part of the issue?
AEM Forms Designer cannot be purchased as single application, it's bundle to Adobe Experience Manager (AEM) Forms. You can request access here: Adobe Experience Cloud | Sales Inquiries
However, if you already have a license number for LiveCylce Designer ES4 you can use its serial also for AEM Forms Designer. A trial can be downloaded here: LiveCycle Blog: AEM Forms Designer Demoversion//AEM Forms Designer Trial
For a better overview about AEM look here: AEM Forms FAQs | AEM Forms Frequently Asked Questions