How do I enable the Omnibar search behavior you describe? When I enter "a" in the Omnibar, I see amazon.com in the Omnibar drop down list, but when I hit tab, Chrome just highlights the next item in the drop down list. It doesn't search Amazon. Have you manually added Amazon to Chrome's "Manage search engines" list?
Firefox has something similar: "Keyword Searches" bookmarks. I define my own search shortcuts, such as "am" for Amazon, "imdb" for IMDB, "nf" for Netflix, and "w" for Wikipedia. Using "am Harry Potter" or imdb or nf or w will use those respective website's own search forms to find "Harry Potter".
https://support.mozilla.org/en-US/kb/how-search-from-address...
http://kb.mozillazine.org/Using_keyword_searches