Actually, you can run the game using the Wine compatibility layer (or similar tools like Bottle). I play Gacha on Linux myself without any problems. In fact, this is the method that Gacha Nebula also recommends on its supported devices page.
Now, as for native support itself, I’m not sure. Linux can be a real headache for newcomers, because there are several ways to package an application (.deb, Flatpak, and AppImage are a few that come to mind), and I don’t even know if Adobe Air supports packaging formats other than Windows .exe and Android .apk.