I am using Stack Overflow; it is a very good site for information exchange.
I want to chat with experts. I am a Flex developer, and I want to chat (discuss) related topic with experts. Can you tell me how can I proceed?
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I understand that you want to chat with experts. Now ask yourself, why would experts want to chat with you? I don't want to imply that you're uninteresting, a poor conversationalist, or a nobody. Rather, understand that there are thousands and thousands of Flex developers, and only a few experts. If they spent their time talking about Flex to anyone who wanted to chat, they'd have no time to do anything else!
Chat can be used to engage other developers 1-on-1. As such, it's not very permanent, and it's not useful for people outside of the conversation. Stack Overflow, however, is permanent (thus far), and it is useful for many people for a long time. An expert would be more likely to answer a question in public on Stack Overflow than to answer a question in private via email or chat.
Also ask yourself why you need expert opinions. On Stack Overflow, content is king - Whether you get your answer from a noob or an expert, you get your answer. There's no need to specify that an expert would need to reply, anyone can post a correct answer.
Just ask your question on Stack Overflow like all the rest.
See Where to post questions asking for expert opinion? for a similar request.
How can I proceed?
Under no circumstances should you use the Q&A format on the main site for chat or discussion. It's just not allowed, and for good reason (see the other answer here).