Actually, I started a 3rd party Flash-based page many years back, and the web visitors normally find my website through a long-tail keyword that they search on the browser - they someone get referred to my page instead.
Thus, apart from social media, etc, you can also ensure to optimize your page as well - make sure it has a proper description, title, and a brief explanation of the game, as those would be useful in attracting natural/organic SE traffic instead.
Put a comment box below, if possible, and your gamers can chat with one another easily while gaming on the Flash page.