get diskaid, navigate to var/mobile/applications and find the folder with the kindle app, then browse to the .app and look for the background image, simply replace with ur own BUT try and keep it on the same size and filename
Gotcha. I have tried that route, but I cannot find a background png or image for the Kindle iPhone. That may be why it is just a white background in the app itself. I do see the iPad background images. Thanks for your help. I guess it is a no go.