You can also run Syncthing on a jailbroken Kindle. That opens up a world of possibilities!
I've been experimenting with Syncthing on Kindle ( https://github.com/Darthagnon/syncthing-kindle ), but have had no luck seemingly because the Linux kernel included is too old and doesn't support network connections, or because the CPU is too weak. Is there a project other than the one I forked?
I switched over to an Onyx Boox reader, so I don't have a Kindle anymore. But I definitely used the same project as you. I used a Kindle Paperwhite 11th gen. The linked project says it works with Kindle Touch, which is VERY old, so I don't think you're having network issues.
It's been a while, but I think I enabled SSH on my Kindle and set it up that way. I started Syncthing via KUAL, then used an SSH reverse proxy to configure Syncthing on my laptop.
It -was- kind of a pain, but once it was good, it was good!