As for simply buying a new assembly (soldering a new micro-USB connector will be almost impossibly difficult to get working successfully), contact Amazon Customer Service and see if they can give you information about ordering parts. It's likely you'd have to replace the entire motherboard (essentially the whole Kindle Fire innards) to repair the unit unfortunately.
Since Amazon is the only source for Kindle Fire units, they will also be the only source for spare parts (assuming even they can source them).
Soldering a USB connector onto your own existing Kindle motherboard is likely to be an exercise in frustration resulting in the eventual destruction of the motherboard, unless you have a well equipped repair bench and the experience/soldering skills to successfully complete the repairs.
You should contact Amazon customer support and ask them about buying a new motherboard for your Kindle. (NOT talking about warranty service, simply about buying spare parts for the Kindle.)
Replacing the motherboard would be a relatively easy procedure following the guides here on iFixIt