Those videos and photos that are being saved on your device are just cached files that are streamed to your device while the bird is in flight. They are quite low quality and almost every time you're going to be better off pulling the full files from the SD card. The only situation that I can really think of where you'd want the cached files is if you lose the drone during a flight and it's unrecoverable.
That being said, if there's no setting within Litchi to cache videos and photos, you're probably SOL. Take a look through all the settings and preferences. If it's not there, put in a request with the app developers to add the feature.
