First thing is to try rebooting your router. That is very often all that is needed.
Also try rebooting the Kindle, by pressing/sliding the power switch and hold it in place for 20 to 30 seconds before releasing it, then wait for it to reboot itself.
Also, you should visit somewhere like a McDonalds and try and see if it will find & connect to the wi-fi in there.
1. Restart your Wi-Fi connection on your device. Swipe down from the top of the screen and tap Wireless, and then tap Wi-Fi. Next to Wi-Fi, tap off, then tap On.
2. Restart your device. Press and hold the Power button for 40 seconds or until the device restarts automatically. If your device restarts automatically before 40 seconds has passed, release the Power button. If your device does not automatically restart after 40 seconds, press the Power button to turn it on.
3. Move closer to your router. From your device, check if you can connect to your Wi-Fi network. If your network doesn't appear in the list, tap Scan from the Wi-Fi menu. If you still don't see your preferred network, you can add it manually to your device.
4. Use Channel 1-11. Check that your wireless router is set to use a Wi-Fi channel from 1 to 11. Please refer to your Internet service provider, if they provided your wireless router, or the router manufacturer, for additional help.
5. Restart your router and modem. Unplug your modem and router, wait a full 30 seconds, and then plug the modem in. After your modem turns on, plug in your router and wait for it to turn on.