Amazon pulled their old windows phone 8.1 application few days back from the windows store and just now, windows 10 mobile version of the it has hit the store and you can download it. The application description says that it is supposed to work only on windows 10 PCs but one can easily install it on their phones as well.
Do not get your hopes up though as it is nothing but a hosted web app but it will definitely stop people from freaking out by not finding official app from amazon on the store. We are quite hopeful that a proper app is in the works, just like the one found on iOS and android.
I personally loved the barcode scanner feature found in windows phone version. Other features that we would like to see in future updates include notifications for shipments and for things like Amazon Days. Addition of pricing alerts and tracking would be nice too.