Hi Matt,
You most likely just need to re-solder the connections of the USB socket to the motherboard. Manufacturers nowadays use lead-free solder which is not as durable and certainly not as flexible as the leaded version. If you open the Kindle, just gently wiggle the socket and if it moves then you definitely have a dodgy connection to the board.
If for some reason your pins are bent you can always, try to bend them back to straight or order a new USB socket and solder it on.