To install Flatpak, set NixOS option services.flatpak.enable to true by putting the following into your /etc/nixos/configuration.nix:
services.flatpak.enable = true;
Then, rebuild and switch to the new configuration with:
sudo nixos-rebuild switch
For more details see the NixOS documentation.
Flathub is the best place to get Flatpak apps. To enable it, run:
flatpak remote-add --if-not-exists flathub https://flathub.org/repo/flathub.flatpakrepo
To complete setup, restart your system. Now all you have to do is install some apps!