Amongst the other casualties and missing apps after the Lollipop upgrade was the "Kindle for Samsung" app. Pretty much anything from Samsung disappeared after the Lollipop update.
BEFORE some dolt says go to the Google Play store, the Samsung-labeled version is what you need to get your free monthly e-book that Samsung said they would give you back when your Note 3 was running Android 4.x. When the Note 3 first came out you used the Samsung Store to get the books. Then Samsung switched to a custom version of Kindle and you could pick a free book from four books that were offered each month. Never any big best-sellers, but some were entertaining.
Amazon suggests going to the apps.samsung.com site using the base, non-Chrome, browser. You should then be able to download it and "side load" the APK file. All that gets me is a redirect to the general Samsung web site.
I happened to have a backup of SOME the apps on my phone from the Android 4.4 days. Against all odds, the Samsung Kindle APK was there. I managed to "side load" it. However, it crashes as soon as I try to run it.
I want my free e-books.
Did you contact Samsung about Samsung's custom app?
I think you can get the Amazon Kindle App via the Amazon Store. Probably won't get you free books, but worth a try.
Samsung live chat rep is who sent me to "apps.samsung.com". I wasn't able to try the link while I was in the caht (no phone service in my office). so I didn't know it was no good until much later. Google is where I found the mention on Amazon's site directing people to the same bogus address.
More Google searches later, it appears that Verizon, alone amongst the other providers that sold the Note 3, intentionally disabled Galaxy Apps, and other Samsung-provided applications in the Lollipop update. I am sure they must have been a threat to the Verizon cellular infrastructure. (sarcasm) More likely a threat to Verizon-offered services profit margins.
Color me not surprised. Verizon seems to reduce the features on their version of just about every phone they sell, compared to other carriers.
I am also not surprised Samsung seems to have dropped the ball on their end as well.