First of all, you need to log in to your Amazon Developer Account. You will be taken to the dashboard page. Click App & Services, and then My Apps:

Select the app that you would like to update:

Click on the Images & Multimedia tab:

Scroll down until the end of the page, and then click the Edit button:

You will now be able to edit your current screenshots, and drag or select the new screenshots that you want to upload:

You can upload up until 10 screenshots in Amazon. 

Amazon allows you to upload images with various dimensions. A quick tip though! If you already prepared the images for Apple App Store screenshots and Google Play Store screenshots, you can use the 1242 x 2208 image and simply resize it to 720 x 1280 (one of Amazon's dimensions requirements) and the image won't be disoriented. Of course, if you'd prefer to prepare the image in a bigger dimension for Amazon that would be up to you :)

Once you've uploaded your screenshots, scroll down again to the end of the page, and click the Save button:

After that, you can go ahead and re-submit the app: