Looks like Duolingo uses Google services to recognize speech. My best guess would be to try the web browser version, otherwisee not sure if there's a way to use the app without g services (or at least Google speech services).
Discussion
If this is the case then sandboxed Play Services will be required. Uninstall DuoLingo and install all 3 Play Services dependencies. Install DuoLingo again.
If you're concerned create a secondary/multiple user and install there to isolate it and be able to turn it off/put the user back at rest (encrypted) by pressing the 'End Session' button on the lockscreen or power menu.