In regards to the tablet, I’m thinking about buying an Amazon Fire HD 8 though I’m open to any and all recommendations.
As for the distro, I’m fine with Ubuntu or Linux Mint (or for that matter anything that you may recommend).
For the ebook reading software, I’m leaning towards using Foliate since it supports kindle, epub, and pdf formats, not to mention that the UI is great and intuitive.
You can’t do that. Installing custom ROMs on Android devices is very different than installing an OS on a desktop/laptop. Most devices don’t allow changing the OS at all, most of the ones that do don’t have any Linux builds, and then you’ll be stuck with whatever distro you’re given (probably UBPorts or maybe PostmarketOS) rather than choosing your own.
I was thinking of using this guide to install LineageOS on Amazon Fire HD 8 tablet: https://frontpagelinux.com/tutorials/how-to-install-lineage-os-on-amazon-fire-hd-8-tablet/
Kindles are really hard to root. Use XDA Developers forum for this kind of thing. https://xdaforums.com/t/fire-hd-8-2018-only-unbrick-downgrade-unlock-root.3894256/, which is what that guide is based on, looks like it only works for the 2018 version and seems way more difficult and risky than most ROM installations. Also, that won’t install Linux, just a different Android version.