I have to remark that, not only for Flash video (.flv), this solution can be used for ALL file types which are not to be downloaded. Its quite helpful for stopping users downloading games, mp3s, etc directly from the internet.
The solution is actually about how to do it instead of "is it possible?". Luckily the creators of Dansguarian (the source system in Endian, Smoothwall etc.), thought of the solution, but preferred to keep it disabled as default.
If you try to disable Flash video MIME, as the MIME standards are rather out of date, it generally disables all flash based activity in pages including .swf, related bank and other flash integrated web services which is a useless solution.
Although it doesn't show directly on Endian interface, its underside software Dansguardian, fully supports ban of extensions via a ban list stated deep inside the linux file system. At this point I must warn that although Endian's filters are built on Dansguardian, their folders are in different locations.