Have a flat do I have to replace all the tires
First of all some flats can be fixed. If the other 3 tires are worn go ahead and replace all the tires. If they are nearly new you can replace one tire.
From the Tire Rack. Audi, As published in their vehicle owner's manual, "rolling radius of all 4 tires must remain the same" or within 4/32 inch of each other in remaining tread depth.