If it is a red board, mini USB connected FT232RL adapter (
looks like this), you need a 1.8v regulator such as an AMS1117 1.8 to tune down the 3.3v signal to 1.8, you connect the right leg of AMS1117 to 3.3v, then the middle leg to VCC of the serial adapter's board. Left leg is to connect it to ground.
Once that's done, you'll have a 1.8v signal for RX/TX, and only then you connect those to the Kindle. It might be a little too late for your PW3 though assuming you sent 3.3v signal through it, possibly killing the serial interface.