Use moving scarecrow type tricks to scare them off. A holographic owl mounted near the Flytraps can scare them as the eyes seem to move. There are hanging hawk cutouts you can get that you can set up on lines that flap their wings in the wind.

You might try researching spices and herbs that are distasteful to birds in general and sprinkle them on and around the Flytraps. Birds are scared of loud noises, snakes, cats, dogs, and motion. Use nature or simulations to your advantage to keep the birds away.