APK (application package file) is the "android-app.apk" file which you can open to install an app. It is the Android equivalent of a Windows "application.msi" installer.
Normally you don't see it, since Google Play/alternative appstore downloads the .apk invisibly during the install process. (That is why we use appstores, so we don't have to mess with this stuff.
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I have found it here:
http://www.androiddrawer.com/3092/do...4-1-1-app-apk/ so you should be able to download that on your Kindle Fire and open "ColorDict_4.1.1.apk" to install.