I have downloaded the flatpak repository but don't know what to do next.
As noted, flatpak is included in Zorin OS. So, you should not need to download the file and do anything next.
However, if you have removed Flatpak at some point or if Flatpak is not working properly, please open a terminal and run
sudo apt install --reinstall flatpak gnome-software-plugin-flatpak
Thank you for helping.