If the content is being loaded dynamically into the Flash movie it's very likely occurring over a standard HTTP request. Wire Shark may be a little overkill for detecting something like this. I'd recommend using a utility that will capture HTTP, such as Charles, HttpFox, or screen-scraper. Using one of those tools, watch the HTTP requests that occur while the content is loading. Once you determine which request it is it's likely you can just replicate it in your code.
That said, I've also seen cases (though not very common) where the data loaded into the Flash movie is done with a binary protocol, which makes things a little more difficult. AMF is often the protocol used in these cases. Charles proxy will detect this protocol, so that may be the tool to use in this case. A while back I wrote a blog post on extracting data that's delivered via AMF. It deals with a Java library, but you may be able to find something equivalent in .NET.