Split test two fliers.
Make them exactly the same except for the bonus code and one other variable. That variable can be color, ad copy, image, etc.
Then figure out which one had a better
conversion rate. That becomes your new test.
Next time you do a flyer distribution, change one variable and test another flyer design. If it performs better, it becomes your new test, and if not, then you try another change in an attempt to beat your
conversion on the old flyer.
Rinse and repeat.
As you continue doing this, you'll figure out which elements increase
conversion rates, and you'll eventually be able to design flyers that convert tremendously better than your original flyer.
The trick is to only change one variable at a time, track your results, and continuously improve your
conversions.