How to get updates for apps which use Google Play on my Kindle Fire? A number of apps on my Kindle Fire indicate that updated versions are available and prompt me to "tap here to update" or words to that effect. The trouble is this: so far all the apps with updates -- even those purchased directly through the Kindle Store -- will open up Google Play and ask me to download the update package. This, of course, is impossible for me to do since the Kindle Fire is unwelcome at Google Play. 

Bringing up the app's info page in the Amazon App Store app just gives me the option of launching the already installed version, but there's no option to download the latest update.

So, how can I update these apps? Must I hunt down the APKs for each app individually? Shouldn't these apps be opening up Amazon's App Store rather than Google's? Is there a system setting I can change that makes them do so?

I can't seem to find any mention of this type of problem anywhere; Google just spits out results about installing apps rather than updating them.

My Fire was previously rooted but I haven't re-rooted it since the last time Amazon pushed out an update to the OS.
I have a rooted B&amp;N Nook Tablet and see this same sort of thing.  Applications are identified primarily by their package name, and most app authors don't bother using a different package name across markets.  My nook has the B&amp;N Market, the Amazon AppStore, and Google Play.  These three markets tend to get into a game of tug of war, each trying to update apps to the version they see as most current.  The thing to keep in mind is that, just because that market says it has an update doesn't mean it really is a newer version of the app than what you have, just that the version number is different.  I get this quite a lot with the revisions of Netflix on my nook as Google Play likes it at one revision number while the B&amp;N Market likes it at another.

If your goal is to be completely rid of update notifications from apps you can't update, your best bet is to factory reset your Kindle.  A complete factory reset will get rid of Google Play and will eliminate the update notifications. Then you can re-install the apps you've purchased via the Kindle's native app store.

Alternatively, you can re-root your device and let Google Play updates complete.  I don't think this is the best solution for you, though, since your device could end up like mine with different markets each clamoring to apply their own updates in a continuous loop.