If you use Flash Media Server, you can stream video and create chat apps
with this server.
And if you don't want to spend a ton of money on Flash Media Server, especially since you already have streaming your video working, you may need to have the number of viewers recorded via something like PHP, Java, etc. because Flex can't do it.
Each user will get a copy of the SWF delivered to them, so the best you can do is have the Flex app communicate with the server to tell it what video is being viewed, and then possibly update something in a database that can be reflected back to the users. You actually might be able to do this in Flex. Just update the database and then push the total viewing video back to Flex app.