How do I give a Developer access to the Nintex Forms and Workflow Management in Central Admin without making them a Farm admin?
I don't think you can, since in order to access Central Admin, you need to be a farm admin.
There is the concept of "Service Application Administrators" in SharePoint, where someone can access a security-trimmed Central Administration without needing Farm Administrator permissions:
Assign or remove administrators to a service application (SharePoint 2013)
An administrator of a SharePoint 2013 service application can assign additional administrators to that service application. These users are granted security-trimmed access to the SharePoint Central Administration Web site and can manage settings related to the service application. An administrator of a SharePoint 2013 service application can also remove administrators from a service application.
However I don't know that Nintex has this model/capability built-in currently?
I'm almost certain that Nintex wasn't implemented as a Service Application, otherwise Jess Collicott's suggestion would be perfect.
Brian - Which specific Nintex features do you need the developers to access in Central Admin? Note that many configurations that a workflow developer would need are also available from the site settings page. However, there are no Forms specific settings available there. In case you haven't explored it yet, be sure to check out the Nintex Workflow Site Settings:
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