Qt Gamepad module (https://doc.qt.io/qt-5.9/qtgamepad-index.html) is part of Qt SDK since Qt 5.9, but it seems org.kde.Platform/Sdk doesn't bundle it.
For the record, I tried it with org.kde.Sdk//5.12
Git commit 1c98c5d7c0feaf7827a19237d06edb91ea93f619 by Aleix Pol. Committed on 17/03/2019 at 09:11. Pushed by apol into branch 'qt5.12lts'. Include Qt Gamepad M +12 -0 org.kde.Sdk.json https://commits.kde.org/flatpak-kde-runtime/1c98c5d7c0feaf7827a19237d06edb91ea93f619