Sorry, this is not going to work with built-in HTTPLiveStreamRecord. Sorry for misleading. The built-in feature will only allow one recording per stream. However it can work with the LiveStreamRecord API, I tried it with the old ModuleLiveStreamRecord, I just had to comment out these lines:
The package with this source is here:
//if (prevRecorder != null)
There is a Flash UI for this. To make two recordings I had to open two copies of it, and set different file name for outputPath in each. It worked in my test, after re-building the module with the above two lines commented out.