Based on some previous forum posts and responses, I'm not sure everyone is aware of this, but you can definitely get Google apps (Gmail, Google Music, Youtube, etc.) running on your Fire without rooting. You just need to install GoogleServicesFramework.apk. I used the one from my Evo and the whole process was very smooth. I have never rooted my Kindle and I have multiple Google apps running. I've linked below to the forum that walks you through the process, however I didn't use the files posted there, I used my own from my Evo.
I also tried to get the market to work and it installs and lets me browse the market, but I can't download anything, so I'm assuming you definitely need root for that to fully work.
As a caveat, I tried this before the 6.2.2 update, but I think it still works.
What about for us that don't have an android or google phone. Is there a way we can still download .apk to the computer and sideload to the kindle fire? I tried downloading an app off the android market but it won't let me since there isn't an android/google phone associated with my account.
Even if I root my fire, do I still need an android/google phone to download apps from the android market?
Without rooting, even though I have an Evo, I still can't download apps directly from the Android market to my kindle. I'm pretty sure the only way that would be possible is through rooting. However, there are alternative markets like and other places to find apps, if you are looking for something different than Amazon's Store.