using the amazon product api, in theory you can build an app for any platform including android. Amazon themselves have already created their own Amazon app for the iPhone, i dont have an android powered phone so I'm not sure if there is an Amazon app available for that.
Of course, it is very possible. The API is there for you to do whatever and however you see fit as long as you follow the terms and condition. With the API you can create any app you want to interact with their service. The only problem you'll have though, is that it might not worth spending precious time on - giving that most people use desktop. I would focus on desktop and aim to convert more rather that creating a mobile app that might not even perform much. Just a thought.
I thought about doing an eBay or Amazon app for Android, Symbian whatever, but the problem is that people don't MAKE purchases via their mobile phones, especially not non-mobile-related ones. Can you imagine anyone buying a plasma TV via a mobile app?!
How about just hyperlinking to start with? ...assuming your layout/main.xml has: <TextView android:id="@+id/Ad" android:layout_height="wrap_content" android:text="dummy" android:layout_width="fill_parent"/> Code (markup): ...then something like: @Override public void onCreate(Bundle savedInstanceState) { TextView theText; super.onCreate(savedInstanceState); setContentView(R.layout.main); theText = (TextView) findViewById(R.id.Ad); linkText = "...buy a <a href='http://www.amazon.com/exec/obidos/ASIN/1430231564/309407659021-20'>book about learning Java using Android as an example</a>."; theText.setText(Html.fromHtml(linkText)); theText.setMovementMethod(LinkMovementMethod.getInstance()); } Code (markup): More details at my tutorial http://code.google.com/p/android-java-tutorial/wiki/StageTwo
I would question the effectiveness of such an app, both in getting approved and perhaps encountering resistance from the Amazon program itself, I suspect that in the future this will in fact be something that will gain popularity, however as others pointed out, most people feel more comfortable ordering from a desktop. Still its an interesting topic.