How to reduce noise? (FlipFlop circuit creates lot of noise)
What you have made is digital circuitry- it switches. Using the same unregulated supply is injecting noise into your amplifier through the battery power. 

Possibly the problem is in the electret microphone front end receiving power from the battery without regulation or enough filtering, but we have no way of knowing what circuit the detector uses let alone redesigning it to work better. 

If my guess is correct, a simple RC filter on the electret load may work: 







simulate this circuit &ndash; Schematic created using CircuitLab