Azoxystrobin is the fungicide, and it is inexpensive and easy to obtain as Scotts Disease-Ex Lawn Fungicide.
For $15 get 10 pounds! An application for a fly trap is 500 mg (about a quarter of a teaspoon) mixed with 8 fl oz of distilled water. Then you water your fly trap with this solution after vigorously mixing it. Do this 3 times per growing season. A 10 pound bag would allow you to treat 30 fly traps for 100 years! It is a systemic fungicide that will protect your plant from rot, but more importantly, it increases your plants rate of growth and the longevity of its leaves and traps.
Here is a research article that explains why. Azoxystrobin is a class of fungicide known as a strobilurin. It is not a fertilizer, but instead the chemical protects the plant from oxidization that naturally occurs due to the wear and tear of photosynthesis and other natural and normal forms of environmental stress. The research article discusses a different molecular form of strobilurin that is equivalent in effect as the more commonly available azoxystrobin.
Azyoxystrobin is a systemic fungicide, which means the plant will soak it up through its roots and then spread it throughout the inside of the plant. The effects of azoxystrobin last for about 30 days, so watering your plant with it once per month during summer is ideal (max 3 applications per year).