Flatpak works just fine on both NixOS and Guix System. Occasionally you might need to expose systemwide SSL certs to the individual flatpaks or something on Guix. When I said out-of-the-box, I meant if you enable flatpak in your nix config, it works without issue. Obviously you need to install it since the only package manager provided by default is nix (or guix).
Direct quote from the Nix wiki:
On most distros, all one has to do is download the .AppImage file, make it executable chmod +x $AppImage, and execute it. This doesn't work in NixOS out of the box though, as AppImage files usually (if not always) depend on certain system libraries in hardcoded paths.
Basically every appimage needs to be run through a wrapper executable that I'm guessing patches the paths. So on top of the app not showing up normally in the DE, it also now cannot be directly run.