It's in the hazard warning switch. You need to replace the switch.
The turn and hazard flasher relays are incorporated into hazard switch.
1996-2001 Audi A4 1998-2005 Audi A6 1997-2003 Audi A8 The flasher is located on the dash above the radio, it is te same unit as the hazard switch.
The turn signal flasher relay is located behind the hazard light switch, which you can access by removing the associated dash trim panel
Replace turn signal flasher
The flasher is right above the fuse box, pull it out, and replace it with a good one.
Inside the hazard switch.
The first and least expensive thing I would do is replace the turn signal flasher. If the flasher is weak, then it could act-up just as you have suggested. The turn signal flasher is a separate system then the four way or hazard flashers even though they use the same bulbs. Generally, the turn signal flasher (which simply plugs in) is located near the steering column but on your model I would suggest you purchase it from your dealer and ask them to print out the picture of the flasher which will show you it's location. I you. Mark
Check: Fuse Turn signal flasher Switch at steering column Bulbs
I've written it up here... http://samboutros.wordpress.com/2007/04/02/2003-audi-a4-bulb-replacement/ Steps, pictures and links to bulbs...
This seems to be a cammon fault with VW/Audi cars. U will need to replace the hazard light switch mechanism which contains the switching contacts. I had to replace same in my last cars (VW/Audi)
I had same problem went to junk yard and got a hazard switch the turn signal relay is in this hazard switch. Removed radio, released bracket, slid out switch and replaced now works fine. I'm a woman and did this so anyone can do it. Provide some more details as to how to remove radio to get to place where you replace the 'Turn Signal' Flasher. Oh, by the way, I have a 2003 Allroad.
It is connected to the back of your Hazard Flasher. I just had to change mine. About $65.00 to $70.00. Couple of clips at the bottom of front panel then it just pops out.