I do not think this is a current feature for the iPhone. But I could be wrong about this. I do not currently see any settings in iPhone when watching a movie that would show the CC during play.
Keep a look out for iPhone Software 2.0 coming later this month. And keep an eye out for keynote tomorrow as I am sure more info on 2.0 will be provided.
The iPhone does support Closed Captioning. Tap General, then iPod, you'll see under Video to options. Start Playing and Closed Captioning. Once you turn it on, you'll be able download and view the Closed Captions in the movie located here on your iPhone.
There are a few movies on iTunes that show [CC] in their description, but I haven't downloaded them to try 'em out. Currently, getting CC's INTO movies are the hard part as there's no easy or inexpensive way to do it so far (The movie above was created by Israel Melendez). You can find a podcast with CC instructions at this iTunes link.
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CC in movies
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