How can I access Chrome's spell-check dictionary?
The dictionaries are available for download from http://src.chromium.org/viewvc/chrome/trunk/deps/third_party/hunspell_dictionaries/. (Files with .dic extension.)
I am not sure if this is related to your request. It appears another developer created an extension to look up words, not sure if the api he founded used the internal dictionary spell-check or not...my assumption would be that the api merely return results from a google query using an advance search feature like "define: example", example being the query/word. Here's a link to the article though it's quite outdated.
http://googlesystem.blogspot.com/2009/12/on-googles-unofficial-dictionary-api.html