I'll tell you up front that I don't use Flash, so this is supposition.

When you say "Flash object" are you referring to the application, or to some
class in Flash that can be instantiated and added to a container?
I'm asking this because, typically, application objects don't appear in the
toolbox. You have to write applicable code in your .NET application to
create a Flash instance and manipulate it through the API supplied by the
application vendor.

I'd suggest you research using Flash with .NET by starting at the Flash web
site and looking for support material on their API.