Do not use bash or sh, just use the uploader script itself -- ./dropbox_uploader.sh
As per standard unix script design, it includes a shebang that points at the bundled bash binary.
This is necessary because unix does not include the currentdir in your PATH -- so when you used "bash" it resolved to /usr/bin/bash which is part of busybox which breaks hard.
Also note -- awkward typing unless you make the config files from a computer. usbnetwork+ssh should work, so should running on a linux PC then copying over to the Kindle.
brianinmaine -- why must users create an app? You can publicly release one so people only need to authenticate an account.