You need to make sure your cord is a 1.8V, not 5 volts. My personal kindle has been tolerant of 3.3v, but 5v will almost certainly burn out your device.
One official site is this:
http://www.ftdichip.com/Products/Cab...BTTLSerial.htm
TTL-232RG-VREG1V8-WE Supports +1.8V TTL level UART signals and +1.8V / 100mA rated power output.
Check out the 'Serial jailbreak' thread in the developer subforum here for more options.
Here
https://www.mobileread.com/forums/sh...d.php?t=267541
and a newer one
https://www.mobileread.com/forums/sh...d.php?t=289497
the forum recommended device, "jim.sh mini ftx" is out of stock on the single boards, it looks like he has stopped making them, but you can also find usb ttl boards, and logic leve converters.
here is a description of that option.
https://www.mobileread.com/forums/sh...&postcount=200
I do have 1 more jim.sh board i could sell, but see if these options work for you too, or you want the cable type.