Using Amazon Instant Video from Amazon Prime on Non-Kindle device
Yes, you can play Amazon Prime videos using flash in the browser. See this thread.

Per the thread, you may have to remove the stock Flash and install Adobe's official version from the market, as well as the Dolphin HD browser.

You can rent movies from Amazon, which presumably use the same framework as Prime videos. It would probably be advisable to rent a movie to verify it works before investing in a Prime membership.