You can do it easily since FlashPlayer 10.1 with SampleData (event) from Microphone.
microphoneInstance = Microphone.getMicrophone();
microphoneInstance.addEventListener(SampleDataEvent.SAMPLE_DATA, sampleDataHandler);
//will contains your microphone RAW sound data
buffer = new ByteArray();
function sampleDataHandler(event:SampleDataEvent):void
{
while(event.data.bytesAvailable > 0)
buffer.writeFloat(event.data.readFloat());
}
An example (with code), recording locally (without any server) and save a WAV file:
MicRecorder, a tiny microphone library by Thibault Imbert
MicRecorder - A tiny AS3 Microphone library on Google Code
An other example (without code), recording locally also but save a MP3 file:
http://unitzeroone.com/labs/rtmic2mp3/