SSL & https connections use a handshake process to validate who is who. The certificate authority controls the issuance of certificates which mostly update on their own.
Things that can effect this is if your devices date is not correct.
As an example the cert creation date is 2015 and expires 2018. Now your systems date & time setting is set for some reason to 2001 so your system is unable to use the cert as you went back in time from the certs perspective ;-}
Now lets say you set the date to 2019 so now your system still can't use the cert as from its perspective it expired!
So start off by making sure your data & time is correct on your Kindle. If you can, see if you can use the Internet time server option that way you'll always be on time (and date).
OK, still no joy what now? Your Kindle's likely needs an update Kindle E-Readers that Require Updates
Here's Amazons help web site for the Kindle: Kindle Keyboard Help