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You have to "forget" that network and connect it to it again with new password. On your Kindle, go to Settings > WiFi and you will see your WiFi network there. Select it and select Forget. Then tap it and it will ask for password. Enter it.
Let me know how it goes.
If this is a Fire tab, then swipe down from top of the screen and tap More or the gear button to access Settings.
Select WiFi select your WiFi network and you will see Forget option there. After forgetting, select it and it will ask for password. Sometimes when you touch the WiFi, it will directly ask for new password
If this is Kindle e-reader, then tap Settings (three bars) from Home screen or press Menu button (if Kindle keyboard). From Settings, select WiFi networks and you will be able to forget the network.
Then connect to it again with new password.
Refer this article (for E-reader)--> http://www.amazon.com/gp/help/customer/display.html?nodeId=201175570
For Kindle Fire --> http://www.amazon.com/gp/help/customer/display.html?nodeId=201730010