U-boot runs on the kindle flash chip (or uploaded to RAM). The SoC should go into Downloader (serial or USB) mode and allow reflashing over serial, at least, though of course without the interactive textual assistance of u-boot running . It may be worth reading the manual for the SoC in your device...
One concern is that only a smaller u-boot (without BIST and fastboot) can fit in the SoC RAM, and it is u-boot itself that initializes SDRAM where it can bootstrap a larger more-capable u-boot version (with fastboot support).
[Beware that I have not read the manual for your specific device, going by prior knowledge from earlier kindle versions, but it should be basically the same.]
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