Posterous has caught on in recent years as a simple but elegant solution. It's easy to get content into it and they support a large variety of formats including Flash video.
Here is the Posterous FAQ page which answers many questions you might have, including verification that they support Flash video content:
You can also purchase a domain and use that in the future, which was another part of your question. There is a page on that describes setting up custom domains on Posterous (and describes it quite well, I should say):