Amazon has their own version of like Google Play Store and from there you should be able to find the silk browser to add it back. I have 2 Kindle Fire 7's and a Kindle Fire 8 and only thing I have ever had go wrong with software disappearing from the Kindle Fire was when expanding software installations to the MicroSD Card, then corruption happens and then the installed software is mysteriously gone or the MicroSD Card will cause it to fail to boot unless removed from Kindle Fire and then added back after the OS has come online with full tablet desktop GUI. Do you know if Silk was installed to a SD Card and disappeared from similar issue to what i had happen?
(*Note: Not sure if Silk will be allowed to be installed to a SD Card as some applications have a rule set to where they can only be installed to internal storage only. )
