I agree with Dr Drib.

The first logical thing to do after an electronic device gets wet is to remove the energy source immediately. An item that is plugged into an AC wall socket should be unplugged. A device that is running on batteries should have the batteries removed. However, with devices like Kindles it is not easy to remove the batteries. The fact that the Kindle kept rebooting immediately after its bath is not good. The faster you can disconnect a device from power, the better, but Amazon made it difficult with the Kindles.

Lithium batteries are notoriously dangerous when they go bad, so like Dr Drib said, get that sucker out of the Kindle and dispose of it in a safe non-combustible manner. Will the Kindle be okay with a new battery? Who knows. The Kindle likely overheated and likely had multiple short circuits in the initial few minutes. I doubt it will ever be totally normal again, but it might be usable.