I don't know how fuzzy your router is and how smart a Kindle is when it comes to connections.
But I do know that all my Android devices refuse to connect if I use the automatic setup on the device.
Simply selecting your network and entering the correct password never worked here.
Instead I use the manual selection of IP address and DNS server in the advanced settings to make it work.
With an automatically assigned IP address all Androids select the first available in the address range, which is my PC.
As my router does not save any of those settings with a corresponding MAC address chaos will come LOL
So forget your network, connect again and set at least the IP address for your device manually.
Try to get connection and it should work.
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power it of, power it back on again.
i disconnected power from the router and powered down and it is fine.. Thanks Vyger.. Just powering it off and on did not work. but the router version worked..