The light should turn on if plugged into any usb port. I was initially tripped up with the 'intensity' dial on the handle, which was set to its lowest position (no light). -- I just confirmed it lights up by plugging into a USB wall wart.
The USB connection is the wrong kind. Even with an adaptor I don't think it would work because I don't think the Kindle Operating system will recognize the Boroscope and load the correct driver. If you are a real geek there may be ways to manipulate Kindle, but it needs more inside knowledge iof the Android op system and the Kindle version in particular.