Kindle Fire - WiFI Not Working
When the device is powered on and in range, it will not connect to any Wi-Fi signals
Hold the power button until prompted to power the device down. Choose to power the device off, then turn the device back on. Simply restarting the device can rectify the issue.
If the previous suggestion does not work, another possible solution to the issue could be to power off the device using the same procedure stated above, but this time when the Kindle is powered off, also power off and reset the router that is supplying the Wifi signal (if possible).
Restore factory settings
Once the two previous suggestions are exhausted and the problem is not yet fixed, it may help to restore the device to factory settings. Once this is done the Wifi connection will have to be setup on the Kindle as if it had never been entered before.
WiFi Analyzer app
The final device-related fix that can be done without troubleshooting the router, is to download the free Wifi Analyzer app. This will reveal any issues that may be due to busy channels or weak signals.