If your Kindle is not showing up on PC, while you have connected both that simply means your Kindle is not recognized by computer. Before indulging in troubleshooting first ensure that you are connecting it properly and working with the right framework.
Following let's check out what you need to examine:
Working status: Make sure your computer and kindle both are turned On and working well, that means none of these is frozen stuck or hanged.
Check USB Connection: The USB ports are placed at the back side of the system the front USB ports or USB port on external devices are not capable enough to detect Kindle fire devices sometimes. So it's better to use the back side USB ports of your system to connect kindle with your system.
Make sure you have required software installed on your systems. For different operating systems you may need to have some special software or add-ons installed for data transferring job
For Mac OS X 10.5 and above versions "The free Android File Transfer application" needs to be installed. Go to android.com/file transfer and learn more about how to follow the instructions.
For Windows XP, "Windows Media Player 11" is required to be installed. You will get the same at https://www.microsoft.com/en-us/download/windows-media-player-details.aspxFor Linux system, an MTP USB driver needs to be installed
After ensuring that your hardware and software are good enough to work further.
If your Mac system is not recognizing your connected Kindle device, you may try the following troubleshooting guide:
If the problem still exists and your kindle not showing up on Windows or Mac. You may contact the Kindle customer support phone number 1-877-690-9305