Your code is fine. You only need to have the script that loads swfobject.js once, in the head element of your HTML doc.
The URI to your MP3 is invalid. I get an error message from this URI: [url=http://home.scarlet.be/muzieklabo/testflashspeler/resources/dwarsfluit01.mp3]*http://home.scarlet.be/muzieklabo/testflashspeler/resources/dwarsfluit01.mp3*[/url]
Fix that, test the URI in your browser, and your player will probably work.
I only see one thing that needs to be corrected. You have a pargraph element with an id of "player1", yet you are trying to write the player to an element with an id of "player", which doesn't exist. They must be the same:bc.. <td height=27><p id="*player1*"><a href="http://www.macromedia.com/go/getflashplayer">Get the Flash Player</a> to see this video.</div>
If you don't need the advanced features, the object/embed method is adequate.
I did change "player1" to "player" but the controller still doesn't show. Is this because of: "player" <-> 'player'? Should I use the ' ' in both cases? http://home.scarlet.be/muzieklabo/testflashspeler/
I was wondering wether it is possible to integrate your mp3 player in a Flash document. Up to now I'm using Hot Potatoes for making exercises for my pupils, but I'd like to do this in the future with Flash. Is it possible to integrate your controller and if so, how should I do this? As I'm a music teacher, I prefer people having control over the audio, rather than just clicking on one single button.