They're saved in the downloads section within the app, not on your iPhone files. However, once you have downloaded a sermon (e.g. audio), you can play the audio from that page without needing to navigate to the downloads section; the downloads section is just there for you to see all your downloads at once.
Are you downloading video sermons? Each video sermon can use around 200MB of data, and therefore, a combination of video and audio, whilst streaming sermons will eventually take a lot of usage. We suggest you to download sermons over WiFi for offline playback to mitigate this.