Hi,
According to
http://www.adobe.com/products/flashmediaserver/compare/, there is a free edition of media servers, but more than likely it is required to have some knowledge on how to administer it in order to use it. If you don't have a time to examine that, indeed, it may be better to buy a hosting with Flash Media Server for a part of your site with the script requiring it.
It also appears that the free edition of Flash Media sever allows only up to 10 simultaneous connections, so if you are expecting you will be getting more users, 3rd party hosting or full licensing purchase are the options for you.