System Updates on the Kindle Fire can be done from the tablet itself without the need to connect it to a computer. To check for updates and update to the latest software version, do as follows:
1. Open Settings (Drag down the notification panel and use the toggle button)
2. Go to Device settings and then tap the System Updates.
3. Now, tap the Check Now button and see if there any software update or not
4. Update your device to the latest software version