In elementaryos 5.1 (Hera) appcenter doesnt show the downloaded flatpak apps or option to download the flatpak app. (even though I downloaded firefox and libreoffice from flathub.org)
How can I enable flatpak apps in appcenter without sideloading?
There is ongoing work to support this. See the developers git resource: Support systemwide flatpaks I can't give a specific date as to when that feature would be ready, but I would hope it would be complete by the release of elementary OS 6.0.
Old post from omgubuntu: elementary OS Now Has Support for Flatpak Apps
You just need to add the Flatpak remote manually or side-load a single app manually from a remote to make applications from that remote available in AppCenter. This is described in the Flathub setup documentation for elementaryOS. To add Flathub as a remote without side-loading, just type the following command on the command-line.
$ flatpak remote-add --if-not-exists flathub \
https://flathub.org/repo/flathub.flatpakrepo
Once this completes, restart and AppCenter will show applications from Flathub.