Kinetic inductance bolometer technology is a candidate for passive submillimeter wave and terahertz imaging systems. Its benefits include scalability into large 2D arrays and operation with intermediate cryogenics in the temperature range of 5-10 K. We have previously demonstrated the scalability in terms of device fabrication, optics integration, and cryogenics. In this article, we address the last missing ingredient, the readout. The concept, serial addressed frequency excitation, is an alternative to full frequency-division multiplexing at microwave frequencies conventionally used to read out kinetic inductance detectors. We introduce the concept and analyze the criteria of the multiplexed readout avoiding the degradation of the signal-to-noise ratio in the presence of a thermal anti-alias filter inherent to thermal detectors. We present a practical scalable realization of a readout system integrated into a prototype imager with 8712 detectors. This is used for demonstrating the noise properties of the readout. Furthermore, we present practical detection experiments with a stand-off laboratory-scale imager.