FS-ATC-Chatter attempts to replicate the behavior of a real world air band radio. By default FS-ATC-Chatter will be using automatic controllers and radio power monitoring. That means in order to hear chatter you must be connected to the simulator, radio power on, and tuned to an ATC facility that is within 100 nautical miles of your aircraft.
If you don’t hear chatter make sure that those conditions are met. Generally, FS-ATC-Chatter will give you and indication of why chatter is not playing with a short message just above the collapse button on the main window.
Aircraft must properly maintain the radio power status in the simulator if you operate with the monitor radio power option (default). Some aircraft designers might not be doing that which will lead FS-ATC-Chatter to think the radios are not powered up. If it works with the default C172 but not a particular aircraft then you should disable the radio power option is FS-ATC-Chatter on the settings page. If it starts working then run with that option disabled and report the bug to the aircraft designer.