Amazon must put their DRM module into the APK file; therefore, you must sign it after that because writing anything in a signed APK file will invalidate the signature. The following link describe in detail how to manually sign your APK file:
http://developer.android.com/tools/publishing/app-signing.html
To clarify the case with Amazon:
1- Export an unsigned APK file using Eclipse and send this file to Amazon in order for them to put their DRM into it.
2- Create a certificate using the keytool utility as explained in the step 1 of the reference. (You must use a command shell (cmd) for this. Don't forget to set up the correct path for keytool.exe. It should be located in the bin repertory of your java sdk; like "C:\Program Files (x86)\Java\jdk1.6.0_27\bin" ).
Instead of creating a new one, you can also reuse the certificate created by Eclipse when you export a signed application.
Don't forget that you'll have to reuse the same certificate for creating an upgrade; so don't forget the various passwords!
3- You must then sign your APK (as modified by Amazon) using the jarsigner tool and after that, you must align it using the zipalign tool; as explained in the reference. Contrary to the two other tools, the zipalign tool is located under the tools directory of your android-sdk-windows directory; so it will also be wise to add this tools directory into your path.