If you install an app from the Play store there is no apk file to speak of. An apk is an installable file type but its not how apps are installed through any markets. The market app or play store app acts as the installer and installs the necessary files. An apk is what you would download and install when you sideload an app....think of it as the installer file.

If you want to sideload an apk of an app available through the play store you would have to find someone who compiled an apk (ie a pirated copy) and posted it online. However, I don't know about the Kindle and whether certain apps can be sideloaded.

 

I disagree with Tim. There is an apk file which contains the complete app and copy protection if any download from all app stores to your device. The install process is built into all file managers I have used. The only problem is finding the apk file. I explain a method below I use which works on all my android devices.

I install the Astro File Manager from the play store on the device which has the app I want to side load. You also need a file manager on the Kindle. I suggest the Es File Manager from the Amazon Appstore. The Astro has a backup program accessed by a leftward swipe called Application Manager. Start the App Manager and select the apps you want to sideload. The app backups are installed in their full installable .apk format in the Backup/Apps folder. Copy those apk files and paste them in the KF memory. You can use a cloud service like Dropbox which is available from the Amazon Appstore or use a computer to copy the app file from the GN to the computer and then from the computer to the KF. Once on the KF use the ES FM to select the file and with one touch it will ask for approval to install it.

You still have the potential problem of activating the app on the KF if it was purchased and not free. Also not all apps are compatible with the KF. I don't have any experience with activation.