To use the swc file in your flex application, include the swc file while
compiling the application.

"mxmlc my_app.mxml -library-path+=/path/to/shineMP3_alchemy.swc"

I have included only the option to include the swc file. There will/might be
other options that you have to pass to mxmlc.

Shine converts wav to mp3. If you want to convert raw sound data in bytearray
to mp3, you have to first convert the raw sound to wav and then convert wav to
mp3.
http://code.google.com/p/speechapi/source/browse/trunk/src/flash/com/adobe/audio/format/WAVWriter.as

You can read this http://www.adobe.com/devnet/air/flex/articles/using_mic_api.html
on how to capture raw sound data and on how to convert to wav.

Some sample code to get you started.
-----------------------------------

import com.adobe.audio.format.WAVWriter;
import fr.kikko.lab.ShineMP3Encoder;

private var mp3encoder:ShineMP3Encoder;
private var rawData:ByteArray;

protected function processData():void {
	var wavData:ByteArray = convertToWAV(); //convertToWAV not defined. You have to do it yourself.

	// 128 is the default bit rate.
	// Allowed values for bitrate are: 0, 32, 40, 48, 56, 64, 80, 96, 112, 128, 160, 192, 224,
	// 256 and 320
	mp3encoder = new ShineMP3Encoder(wav, 32); // 32 is the target bitrate
	mp3encoder.addEventListener(Event.COMPLETE, getMP3);
	mp3encoder.addEventListener(ProgressEvent.PROGRESS, updateProgress);
}

protected function updateProgress(event:ProgressEvent):void {
	trace('% completed = ' + event.bytesLoaded); // or you can show a progress bar.
}

protected function getMP3(event:Event):void {
	var mp3Data:ByteArray = mp3encoder.getMP3Data();
}


If you want to delve into the code and do something more:
========================================================
* You have to get the source code by forking or any other means.
* You'll have to download the alchemy toolkit from http://labs.adobe.com/downloads/alchemy.html
* Follow the instructions to install alchemy on your machine.
* If you have modified the source code in lib/shine, run "make" in lib/shine
  directory to generate the /lib/shine/shine.swc file. Then run the build_as3.sh
  in the project root folder to generate the bin/shineMP3_alchemy.swc
* If you have modified the actionscript source in 
  src/fr/kikko/lab/ShineMP3Encoder.as, run the build_as3.sh in the project 
  root folder to generate the bin/shineMP3_alchemy.swc

NOTES:
=======================================================
I'm not a legal expert by any stretch of imagination. You are using this code
at your own risk. Why is that and why did law come into the equation here?

* MP3 is not a free codec. http://mp3licensing.com/royalty/
* And this is an LGPL'ed code. If you link the library statically into your
application, that too will be come under LGPL or GPL(not sure which one, as i
said earlier, I am not a lawyer).

So, if you use this code and become the next big thing like Google or Facebook,
and you have lawyers knocking on your door, don't blame me; I have warned you.