There are so many reports regarding the Fire Tablet Netflix App compatibility since the early releases, then you open the Netflix App it clearly shows the App doesn’t work.
It appeared to that the Netflix App is not compatible with the Fire Tablet.
But there are some reports that it says this is a software issue, so you can try following steps and those might help to fix if the issues is a software related.
1) Reboot the KFHD by pressing and holding the power button for 30 seconds and allowing it to shut down on its own. Then press the power button again. (This is unlikely to solve the problem but it’s always the best first step in troubleshooting.)
2) Access settings by swiping down from the top of the device. Then More>Applications>Installed Applications. Find the Netflix App and “Clear Data.”