Amazon just released the app today. It's only available in the Android Market, so here is a copy for those who need it.
Kindle for Android (requires v1.6)
Please excuse the lack of pictures. I only have a large screen Android tablet working right now, and it wouldn't really convey the experience you would have.
I really wasn't expecting much when Amazon first announced this app. The Kindle for iPhone app is best described as a very adequate app, and I expected the Android app to follow in its footsteps. But, the Android app actually has fewer features. You have a limted number of options: 5 font sizes, 3 backgrounds, and bookmark. It doesn't have a dictionary, highlights, or notes.
I checked online, and Amazon is promising an updated app with search, dictionary, an in app Store, and the ability to zoom images.
So what do I think? The reading experience is very adequate, but I would not replace Aldiko with this app. TBH, that's about what I expected. Amazon have set a standard of being the second best app on any given platform. Really, the only reason to download this app is if you have a large bookshelf in the Kindle store (and you don't want to bother removing the DRM).
P.S. That's not a criticism. I swear by the eReader Android app for much the same reason.
Update: I've heard from MobileRead that you can't read your own ebooks with the app (it crashes). TBH, I didn't think to try my own Mobipocket ebooks with this app. I had assumed that it would be as locked down as the iPhone app (it is).