It is easy to copy the HTML code of their player and use it on your web-site. But I don't really know how to get a Shoutcast MP3 stream get player in your own Flash player. You may read more about Shoutcast/Icecast and Shoutcast flash players to find out.

And you can always hire a web developer at a freelance marketplace to create web applications and web pages for this. It will be cheaper and you can select an IT professional or a web-design company that posseses the skills you need. And you can rely on the feedback of other buyers that a freelance marketplace provides.