That is a multi-layer board, you are not going to easily re-wire it.
If you must hot-solder, invest in an appropriate sized soldering iron, it will be cheaper than a new motherboard for your Kindle.
We have directions, they are indexed by a Sticky thread here.
I'll save you a click or two:
https://www.mobileread.com/forums/sh...d.php?t=267541
Two things to note -
The directions include links to several different ways to make the serial port connection without using hot solder.
The directions include a link to the recommended adapter.
Which you can purchase from Amazon (who else?):
https://www.amazon.com/gp/product/B01GW2EGEK/ref=as_li_tl
You will also find a thread or two here about installing that adapter
inside of a Kindle (a PW3, but should fit in a KT2).