Try this and then let me know if your network shows in the available networks in the wifi list on the kindle.
>press and hold the power button for 20 seconds and then release.
Then power on and select Wi-Fi from the menu. Ensure Wireless Networking switch is in the on position.A list of networks will appear. You may have to wait a moment as your Kindle detects networks in range. If your network doesn't appear tap the tick box next to Wireless Networking off and on to refresh the list.Tap the name of each of the networks one at a time and choose forget. On the screen prompting you to enter a password, select Forget.
Then press the power Burton for 20 seconds again. Then try your wifi again.