This article tells you how to set wallpaper on Kindle Fire. You have to root your Kindle Fire first.

1. How to change Kindle Fire
wallpaper
www.epubor.com

2. Kindle Fire is a custom Android e-book reader. But you can’t set
your own wallpaper on Kindle Fire. This is because Amazon has
made some limits on it. This article shows you how to set any
picture as wallpaper on Kindle Fire. It 100% works. But you need to
root your Kindle Fire first. Please view this article for rooting
tutorial:
How to root Kindle Fire.

3. Step1 Install QuickPic
QuickPic is an Android app for browsing picture. You can use it to
set wallpaper as well. Visit the link below to download Quick Pic.
quickpic.en.uptodown.com/android

4. Step2 Set wallpaper
Open any picture with QuickPic. Tap and choose “Set as” –
“Wallpaper”. You can adjust the wallpaper size by draging the box.
Please don’t lock the screen before next step!

6. Step3 Revoke permission
Open ES File Explorer and find path:
/data/data/com.android.settings/files/. Tap the “wallpaper” and
choose “More” – “Properties”

7. Choose “Permission - change”. Make the write permission of
“Owner” and “Group” unchecked.

9. Now please lock the screen and press the power button. You can
find the new wallpaper works.
Source: http://www.epubor.com/how-to-root-kindle-fire.html