First of all you need to register at tapatalk.com.
Then you can "build your own" Tapatalk application here, but it's only a customisation of the Tapatalk app. It's a "all-inclusive" app that you can customize. So basically you can't make your "100% own app" using this feature.
If you need to make your "100% own app", then you can read the API specifications here : Tapatalk API Afaik, there is no binary / library, so you have to implement the API by your self.