Flatpak applications cannot directly use the system theme. This happens because flatpaks do not have the ability to use data files or libraries in /usr
(where system themes are typically located). The solution to this was to package themes as Flatpaks, as relying upon the host to have the correct version for every flatpak defeats the portability benefits it provides. These themes are provided as extensions, to the Freedesktop runtime when the extension point is Gtk, and to the KDE runtime when the extension point is Qt.
The theming system requires Flatpak 0.8.4+ and applications using up to date org.gnome.Platform
3.24+, or org.freedesktop.Platform
1.6+, or org.kde.Platform
5.9+.