Is there an API to implement Yahoo chat in Flex? Or at least some calls?
Yahoo Messenger API is not public, so you will not get an oficial API from them for sure.
Having said that, I don't know if there is an API available for FLEX. But I know one for C and one for Java. Both of the open source. So you can try to implement Yahoo Messenger's protocol in FLEX.
Other thing you can try (although I don't know if it will meet your quality standards) is embedding a WebPage supporting Yahoo chat.
Good luck.