What is the response time for FLIR Microbolometer cameras (thermal time constant)?...

The thermal time constant of the bolometer is between 7 and 12 ms depending on the serial number of the Camera.

The thermal time constant should not be mixed up with "integration time" which is a property of photon detectors.
A microbolometer detector is constantly open to incoming radiation, and responds to changes with the time constant.
A photon detector collects energy only during the integration time which is a parameter that is set by calibration.