First Option.... Try the following and see if it works...
1. Press the Source button on the remote.
2. Navigate to and select the Screen Mirroring source.
3. Your TV should display a screen informing you that it is waiting for a device to be connected. This screen will be displayed until your device is connected.
Now you just need to set up the device (kindle) to connect.
Second Option... Also you can try...
1.) Switch on your Smart TV (yes, I know obvious, but you would be surprised.)
2.) Next press the "Menu" button, and then select "Setup".
3.) Now select "Network"
4.) Then "Bluetooth settings"
5.) There should be the option "Discoverable".
6.) Turn the TV "Off" and then back "On" to make sure the connection holds.
Third and Last Option... One more....
1.) Make sure the tv is "on".
2.) Next press the "Menu" button, and then select "Setup".
3.) Now select "Network".
4.) If Network Type is set to "Wired", select "Network Type", and then select "Wireless".
5.) Select Network Setup.
6.) Next select "Wi-Fi Network" or "Select a Network".
7.) Wait a few seconds for the TV to scan for wireless networks in the area.
8.) Select the name of your network in the list.
9.) Enter your "Wi-Fi password", then push the "blue button" on the remote.
10.) Wait to connect your Smart TV to your Wi-Fi.
11.) "Switch off" and then "Switch On" your Smart TV to make sure the connection holds.