Do kernel-level anti-cheat measures even work if I'm running Steam as a Flatpak + Using the game under Proton? I (naively, perhaps) assumed the security sandboxing model of flatpak would restrict that level of access.
If you're running under proton, it can't work. Proton/wine are not virtualizing a windows kernel, they are intercepting syscalls/library calls and running the equivalent linux code.
Some anti-cheat has clients for Linux (the ones that don't generally just disallow playing on Proton). I don't think the Linux ones are kernel level but don't quote me on that.