If you need a full screen webchat have you tried using the Shareable URL of the webchat? That one is already in full screen mode. You can find it under the [Integrations > Webchat > Preconfigured] section of your bot in the BP Cloud dashboard. Alternatively, if you need this to be under your own website, you could also take the source code of that Shareable URL page (which contains the necessary settings for full screen) and host it on your web server.