We managed to install it, after some difficulties.
We had to run the android SDK manager tool as administrator, to succeed to install the kindle fire prerequisites.
We found that we could not install the driver, using the instructions given.
We ended up delete all devices related to fire/android, INCLUDING hidden devices.
Upon enumerating the android kindle, again, we used device manager to install/update the device drivers. To do that we searched for the drivers
First we installed the composite and then the amazon driver. This required a PC hardware restart.
When the PC restarted, we saw that the kindle fire device did prompt us to accept the PC as a trusted ADB debugging partner.
running android studio as administrator we can now run the app apparently, on the now listed device – after another prompt on the device itself.
we can now at least run our azure mobile app: