Hi,
I'm not a Flash expert but I was researching something similar and I might have some information to help you...
AxShockwaveFlashObjects is a COM library to allow you to integrate Flash content into your COM (or .NET) application. I'm guessing you've already seen the sample app here: www.csharphelp.com/2006/02/using-flash-with-c/
(Couldn't make that a link as I'm an unregistered user and only allowed 1 link per post- sorry!)
It appears that even if you have added the component correctly in Visual Studio, an error can still occur when running the program. The workaround (given here) is simply to include the AxShockwaveFlashObjects DLL in your application directory. (You can download the DLL via that link too.)
Hope this helps!