The development flatpak build had been broken for a while, but I fixed it today. You can find instructions on how to install it at: https://www.gnu.org/software/pspp/get.html, under Development.
Also, I discovered that you can run the CLI from the flatpak (previously I thought Flatpak only worked with GUIs), by typing "flatpak run --command=pspp org.gnu.pspp".