Flatpak can be installed from the community repository. Run the following in a terminal:
sudo apk add 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 Alpine.