There are a few ways your Android app can upload sounds to SoundCloud:
The standard Android sharing flow is very generic - it does not assume that the SoundCloud app is installed on the phone and will work with other types of applications handling audio data as well. This is made possible by Android's intent system which allows applications to pass data between each other.
Use explicit intent sharing if you want to integrate more tightly with SoundCloud - the advantage being that you can set additional metadata (such as genre or BPM) for your audio file. Your app will need to make sure that SoundCloud is installed on the phone and prompt the user to install it if not.
If your integration requirements are more complex than just sharing sounds we recommend using our Java API wrapper along with Android's account manager system. This works by requesting an access token from the Android account manager and is documented along with some sample code in the github repo soundcloud/android-token-sharing.