I would have used a homemade adapter on a chip FT232RL as advised by
Sir Alex.
1.8V internal voltage from the Kindle is connected to pin 4 (VCCIO) FT232RL.
When using 5V TTL, you may damage the serial port of the Kindle.
Datasheet for FT232RL -
http://easyelectronics.ru/datasheet/FT232RL_V202.pdf
scheme of the adaprer similar to this one:
http://dorkbotpdx.org/blog/feurig/a_...gramming_board
But you need to connect to the device only: GND, TXD, RXD, and 1.8V (to Pin 4 FT232RL) from Kindle.
You can use any external voltage 1.8V, connected to GND & VCCIO of the FT232RL.