We don't provide any PDF exports, but CB Privacy can provide a standardized JSON format for exporting the users data. If you need to push data to an external service though you ideally should use CB Auto Actions for that. So for example after a user registers you could use a Request action to send a HTTP request to your external service with whatever data you need to send. This would entirely avoid the user needing to do anything and would be automated.
If you still need PDF export the only thing I can think of is to use CB Content Bot and add substitutions to a Joomla article then turn on Joomla's print button. From there they can save as PDF (all modern browsers provide this). There's probably 3rd party Joomla extensions that can also provide PDF generation and if they support Joomla content plugins you'll be able to easily substitute in their profile data. Take a look at the below tutorial to see how substitutions work.
www.joomlapolis.com/documentation/279-community-builder/tutorials/18353-using-substitutions-throughout-cb