This seems to be the exact problem as in
LPS-777. However ,as it can be seen from the attachment, it affects Flash 10.3 too.
The problem is that the file(s) never get uploaded. Everything else works as expected.
I have tested in FF 5.0 and Chrome on my Linux and Liferay 6.0.6 GA, both had this problem. But tested on a windows platform worked just fine.
The Classical (old single upload) works fine.