For what it's worth, this has been happening to me on a Google Nexus 5 as well. Like you, I use the Kindle app to read books on my phone (cause my Kindle bricked itself outside the warranty period). I have yet to find a solution. It's annoying, because the notification remains active way too long: by the time it disappears, if I've reached that part of the page!
Anyway just wanted you to know you're not alone, and it has nothing (or next to nothing) to do with your phone and everything to do with the app.