Question: Is there any way to export non Camera Roll or Photo Stream photo albums from an iPhone to a PC? There are a bunch of "free" software online than can do this, but they all require you to buy the software to transfer the photos, or they can only transfer a few photos before needing to buy the software.

The iPhone is hooked up to the computer right now and I can browse the DCIM folder, but those are only Camera Roll pictures. I'm not willing to jailbreak the iPhone either as it's not mine.

Answer: 
The application keeps you logged in to your account once you log in unless you log out, but if you do anything that would require a password entry like managing your wish list, a Touch ID prompt comes up giving you the option to use your fingerprint instead of typing in your password
Settings>Passwords & Accounts>Website & App Passwords>Tap “+”
 then type www.amazon.com
Then type username (your email address)
Then type a password of your choice

Worked for me. IPhone 6s iOS 13