Diffuse correlation spectroscopy (DCS) is a promising technique for noninvasive measurement of blood flow, especially for cerebral blood flow where other noninvasive techniques have shortcomings. Conventional DCS often requires multiple simultaneous measurements to enhance the signal-to-noise ratio (SNR) especially when probing deep into the brain with large source-detector separations where photons are scarce. However, this limits scalability when using discrete optical detectors. This study demonstrates the application of the 500 x 500 single-photon avalanche diode (SPAD) array, SwissSPAD3, coupled with a custom field-programmable gate array (FPGA) design, which enables significant increases in SNR compared to conventional DCS systems. We validate the fiber-coupled SPAD camera system against a lab-standard CW-DCS system in two-layer liquid phantoms and in human measurements, and demonstrate robust blood-flow tracking at source-detector separations up to 3.25 cm. These results support SPAD-based parallel detection as a scalable route to improved deep-tissue DCS performance in humans.