How to repair my charging port

This is a pretty common problem with the Kindle Fires. The USB port is poorly designed and comes loose from the circuit board easily. It usually requires the port to be resoldered (or a new port soldered on) in order to fix it. Unless you have pretty good micro soldering skills, you'll need to take it to a repair shop for repair. There are also a number of people who offer a mail in service to repair this (check eBay).