To install Flatpak, enable the ~amd64 keyword for sys-apps/flatpak, acct-user/flatpak and acct-group/flatpak:
echo 'sys-apps/flatpak ~amd64\nacct-user/flatpak ~amd64\nacct-group/flatpak ~amd64\ndev-util/ostree ~amd64' >> /etc/portage/accept_keywords/flatpak
Then, install Flatpak:
emerge sys-apps/flatpak
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!
Note: graphical installation of Flatpak apps may not be possible with Gentoo.