Absolutely, positively not. A 3.5mm audio jack puts out an analog signal at a level that can drive headphones. A USB headset connector wants to eat bits. They are made physically incompatible because, among other reasons, they are incompatible.
While I'm sure that there are pieces of hardware that will do this, they have to be active, converting the analog signal to digital to feed the headset. At this point, you are converting digital (in the source) to analog (at the jack) to digital (in the converter) to analog (in the headset). Guaranteed loss of quality.
I had a strange thought, but I doubt it will work. Which type of Kindle? Does it have a USB port (it will be much smaller, but you probably have converter cables around...