I have been informed the instructions below no longer work. It seems most people these days just install the Shark Codec Pack for Windows 7 and flv playback is supported (supposed to be...I personally do not use this codec pack).
Here's what I did to be able to play .flv (Flash) files on Vista Media Center.
1) Install FFDShow. In my case, I just installed Vista Codec Package 5.2.2 Final
Whichever you choose should be fine. I got the Vista Codec Package from here:
Caution - Once I did this, I noticed I lost audio from streamed movies. The codec package may have installed something that disrupted my AC3Filter. After reinstalling AC3Filter I got my audio back in movies. Always be careful when installing codecs. Installing over existing codecs can cause problems.
2)Edited the registry to add this:
Under HKEY_CLASSES_ROOT\.flv create a new registry string REG_SZ called "PerceivedType" and name it "video"
If you want to run a file to do this download this zip, extract it, run the .reg file (when prompted to merge in registry choose yes).
3) Next I copied a test .flv file to Public\Videos folder. I right clicked the file and chose 'open with' and set it to 'always open' with windows media player. When you open the file, WMP may say 'do you really want to open this extension' click OK, and the vid should start in WMP.
4) Next, I went into Media Center, Video Library, found my sample file, clicked it and it played.