If you try to call a function within Flash from Javascript and that function has the intention of calling a FileReferenceList.browse() it’s not going to work. It’s a security thing. You need to use an in-movie button. Even if you have the JS call a function which calls another function that calls FileReferenceList.browse() it’s still not going to let you do it. I wasted some time figuring this out. Just give up.

This guy had the same issue: http://kevinmusselman.com/blog/2009/01/multiple-file-upload-using-flash/