Yes, it is possible to use Chromecast with FREEDOME on your devices. On Android, however, you need to set your WiFi network as a trusted network in FREEDOME (Freedome > Settings > Trusted Wi-Fi networks) to allow Chromecast to connect to your Android device via the local network.
You must use screen mirroring when you use Chromecast with FREEDOME. If you’re casting the content, what actually happens is that your device sends the link to the content to your Chromecast device, and the Chromecast device then downloads the content from that link. In this way, it totally bypasses your device with FREEDOME.