The K4 and K5 have a 1K series resistor on both Rx and Tx. The K3 may be the same. The kindle Tx cannot sink enough current to bring the SoC side of its 1K resistor down to a logic zero.
I used a series diode, to allow the kindle to pull Tx down to 0.7v (good logic zero), then on the serial adapter side a 20K pullup resistor to 3.3v (or 5v). Less than 20K pullup will not give a good logic zero.
That does not seem to be a problem here though because you seem to have good output.
The K4 and K5 do NOT get a good ground from the serial connector. It is better to get a ground from elsewhere, like the USB cable.
On a K3, I did not test this, but you might have a voltage level problem on the SoC side of the internal pullup resistor, if you are supplying too much current.
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