Why not grow it yourself? I'm sure you've heard of angel.co I'm sure you can find a good network there for investors connected to Amazon in many ways.
But if not, either way you put in a disadvantage if you are the one pitching for the sale. Look for investments instead and make firms bid for you, you never know if a company you haven't thought of or heard of sees value in your assets.
Best of luck.
Many large corporations have both Corporate Development departments and Venture Capital arms in order to handle opportunities to work with and/or acquire small companies. I'm not sure specifically how Amazon does this, and there is really no "standard" approach. Many companies have different venture groups under them with obscure names meant to sort of hide them from view. Otherwise many people would reach out directly and they would be swamped with deal flow that was not highly qualified.
Have you actually built anything or is it an idea only? I would say it's unlikely to attract their attention unless you have significant traction and you can clearly demonstrate how it fills a hole in their offerings or their portfolio, or that you are important to acquire so that a competitor does not acquire you first.
Most of the answer will depend on the details, I'm afraid.
Amazon does not buy ideas. Amazon acquires companies with proven results.
You will need to execute on your idea, gain traction with users, build revenue, and prove that it is a fit for Amazon. Then, they will come to *you.*
If you want to have the partnership conversation with them early in your product lifecycle, make sure you're already hitting targets that are aligned with them and can show that you will enhance Amazon's existing offerings in some major way.
Here are some they purchased outright:
smallparts ( http://www.amazonsupply.com/)
And here are ones they made partial investments in:
LivingSocial (invested $175M between 2010-11)
drugstore.com (owned ~46% of company in 1999)
Bill Me Later
Why not create it. Your exit strategy is to sell it. That's the basics...
When you are successful, companies looking to acquire your business will come looking for you. It may be amazon; it may not be amazon. You may fit amazon's future strategy or you may not. But either way you sold the business.