In order to buy any Android Apps at Amazon, you must have at least one Andriod device registered with Amazon. The only way to do this (that I can find), is to install the Amazon Appstore app onto an Android phone or tablet and then log into your Amazon account on the device.
Once you have done this, you can buy apps and leave them in your library (you don't have to install them). If you don't have a device, you can borrow one from a friend or even use one on display in a store (I found this out while testing tablets at Best Buy, were I bought the Asus Transformer (that I am, painfully, trying to use to write this post).
These are the general steps involved:
[A] On a tablet that doesn't have the Appstore installed:
1. Go to the Amazon Android Apps and Devices page and send yourself an email, where it says "Add a device". Use an account that you can log in on the web, preferable gmail.
2. Use the Settings app on the device to allow installation of apps from outside the Android Market. On this tablet, you open Settings, choose Applications and check the box next to Unknown sources.
3. Open the email from Amazon and click the link to download the Appstore app. When it has downloaded, click on it to open/install.
[B] On a device/tablet that has the Appstore installed:
1. If borrowing a tablet with the app installed, you need to have the friend de-register the app (go into Settings, Applications, Manage Applications, find Appstore and select Clear Data). This doesn't remove the device from his account (so, he can still buy apps) and you'll do this same step later on (which leaves a device registered to your account, but prevents anyone from using the device to purchase apps using your Amazon account).
Once you completed either [A] or [B], run the Appstore app and log in. You can then go to any Android app page using the Android device or your computer (or the iPad) and click to buy an app. It is not automatically installed, but just added to your library.
When you are done shopping from the device, be sure to use the steps in [B-1] above to remove your login information from the device (but leave the device registered to your account, so you can get new apps using the website). If you "borrowed" a device at a store, it's a good ideao to also remove the Appstore app when you are done (same place as [B][1], but choose Uninstall after you do Clear Data).
No pics this time (and if I missed any spelling, I'm blaming the tablet's keyboard, which keeps moving the cursor on me).
ETA: OK, I tried out VirtualBox, which you can install on most computers and laptops: there is an installer for Windows, OS X, Linux and Solaris. If you are a techie, it's not too bad an install -- use the directions I found, install the ISO you are instructed to download onto the virtual hard drive (when you run off the image, choose to install to the hard drive, then skip down a ways in the directions), making sure to create a fake SD card, as the Amazon download requires one. Once it is set up, use the Settings tab to change the boot order, so the Hard Drive is first, the start up the VM.
Click thru any messages, until you see a green lock icon. On the Machine Menu, choose Disable Mouse Integration. Then, click inside the VM and OK a the message that displays. Click and drag the green lock upwards, to unlock the desktop.
Click the menu on the right to see your apps, scroll down to Settings, then Applications and check the box to allow Unknown sources. Press escape a few times, then open the Browser and go to https://www.amazon.com/app-email (or open your email client in the browser and click the link from Amazon). The app installer will download automatically (provided you created an SD card); run it by clicking and dragging on the menu bar at the top. Install the app, open it and log in to Amazon. Once you've managed to get thru the setup, though, you can then buy apps from the Amazon web page and don't have to mess with the Virtual Box program any longer.
There is no doubt a more elegant method, but to back out of an app or window, I just pressed the Escape key until I returned to the desktop. To get out of the VM desktop, press the Right CTRL key one time, then close the VM window. You might want to either Take a Snapshot (a named restore state) or use either the Save Machine State or the Send Shutdown Command when closing the app - that way, if you need to get to the VM again, you can skip some of the installation you just did. Using Save Machine State is the easiest, but snapshots let you back up after installing any app that causes a problem.