Hello, great question! This is a situation where certain tests need to occur in order to properly diagnose the issue. As Ben had asked, are other devices having any network issues? If not, lets test to see if your Wireless Router can properly talk to your Kindle.
Now what I'm about to say may vary based on your internet service provider, and the type of router you have. But the general method to test this; is to log into your router web interface from a device that is properly working. Now, to access the router web interface...the router has it's own IP address. Typically you'll see something like 192.168.1.1 or 10.0.0.1. Try some of either of these addresses to see if you get to a login page for your router. You will want to locate the Admin credentials which is normally found with the documentation on the box that came with the router; or the credentials can be found on the router itself. You'll generally see the username be Admin, and some form of a password associated with that admin account.
Now that we've logged into the router web interface, you will want to look for all of the devices that have/and or are connected to that router. You can find your Kindle by finding the name of your Kindle in the list of devices that has been connected to it. You should be able to click on your device, and you should see another button that say's something like ping test, or connectivity test. When you run that test, the router will indicate weather the connectivity test failed or succeeded. Lets get you to this point before we move onto the next step in determining the root cause of your internet connectivity.
If you have any questions, please feel free to add a comment below this post so we can move things forward for you.