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
Ok, I just figured this out (finally), "and yes it does work". But it seems to be a combination of several of the answers provided above.

Probably the most important thing to point out is Tpoccu's posting.  

"The application keeps you logged in to your account once you log in unless you log out", but if you're anything like me and you log out every time you're finished with the App, continue reading...

The first thing you'll need to do is go to Settings and scroll down to the Amazon App on your iPhone 6 (minimum) with an "Up To Date iOS", then scroll down to "Use Biometric authentication when available" and turn that on as Nura suggested.

Once that's done go to Settings/Passwords & Accounts/Website & App Passwords and Tap the “+” (top right) to provide the credentials that the App needs, and type in www.amazon.com under the Website Address and then just type in your Username and Password as Mr D suggested and you're done.

Then the next time you open the Amazon App and tap the Sign In button the App will ask you if you want to associate the App with the password that you saved earlier, just tap Ok and touch the finger print reader and you will be logged into the App automatically.

I hope this helps!