First a question for clarification:
Are you talking about a SmartApp (an app that is installed via the mobile app and does specific task or function with devices within the ST world) or are you talking a new Mobile App (an app that would be installed on your phone or tablet and all you to interact with all or some of your devices)?
If you’re talking a SmartApp… I know that ST long term goal is to eventually provide a method for developer to make their own SmartApp and then upload them so that they can be easily accessed by other users, and perhaps even a store type setting where you would purchase said apps.
While this is the goal, this still seems a ways off. There is a method for submitting SmartApps for approval, but to the best of my knowledge no user created SmartApps have been approved yet.
If you’re talking a new Mobile App… I don’t know that there is an approved or available method for doing this. Seeing as this mobile app would need to have access to the ST cloud, this raises potential security concerns and so I’m not sure ST would readily approve access in this manner.
I suppose it’s possible you could try to interface directly with the existing mobile app and “scrap” the data from there, but this seems a clunky method.
Another option would be to setup your interaction with devices through Oauth. The downside to this is you only have access to the devices, not SmartApps. Additionally I’m not sure if you can pull data from device (like temp, motion, etc) in order to produce notifications. So I would think this would have to be something that runs along with the ST Mobile App rather than replaces it.