Sorry. APKs? Er...do you mean APPS? (Just in case there's a new TLA I'm not hip to.) Huh! I wasn't aware I could do that, enable download of "untrusted" apps. Will check that out. I don't download many apps.
I did try to pair the Kindle with the car using Bluetooth. I could play music from it, and view pictures on the infotainment system, but Android Auto wouldn't work. Probably fault of the Kindle.
Android apps are packaged as APKs, when you download an app from the Google Play Store (what used to be the Android Market way back in 2008 when I got my first Android phone) or the Amazon App Market (I forget what it's called) you are actually downloading an APK.
By default almost all Android devices will not allow installation from "unknown sources" which means you can only install apps from the official app marketplace that came with the device, but you can change the settings to allow you to install any APK you happen to have directly. If you have a device with an sD card you can just copy the APK to the card or you can just download the APK directly or even E-Mail it to yourself if it's not too big. Generally I will put the APK I want to install in my Dropbox and then use the Dropbox app on my device to download it.
Here are Amazon's instructions to allow installation from unknown sources on a Kindle Fire: [ame]https://www.amazon.com/gp/help/customer/display.html?nodeId=201482620[/ame]
Finding the right APK can be tricky, because there are sometimes different APKs for different devices (tablets or phones) and for different (major) versions of Android. Also when you're installing APKs from random sources you always run the risk you could be inadvertently installing malware (there are actually quite a few sketchy app marketplaces out there).
What I'd probably do if I were you would be to install the Google Play Store on your Kindle Fire, this would allow you to download and install any app you can get there. The Play store won't usually allow you to download a phone-specific app on a tablet (or vice-versa) so you still may not be able to download the My Chevrolet app but it's worth a shot. In any case once you go through that process you will be able to easily access many more apps that you can't get from Amazon.
Note that while I'm not guaranteeing that the above instructions are completely safe but that is a reputable site and the source for the files they are linking is also reputable. If I had a Kindle Fire one of the very first things I would do with it is install the Google Play store using those exact instructions.