The Suzuki–Miyaura cross-coupling reaction is one of the most important reactions for pharmaceutical and fine chemical synthesis, performed using both homogeneous and heterogeneous catalysis. In this work, we cross-link poly(methylhydrosiloxane) (PMHS) with tri(ethylene glycol divinyl ether) to create a versatile and readily accessible gel catalyst support for Suzuki–Miyaura cross-coupling reactions in a pseudoheterogeneous manner. The Si–H units present on the PMHS backbone act dually as the cross-linking site and the reducing agent to anchor and reduce palladium(II) acetate to active palladium(0). The PMHS-supported Pd catalyst is then packed into a stainless-steel flow reactor to create a cartridgelike reactor for the continuous operation of a model Suzuki–Miyaura cross-coupling reaction. We systematically investigate the role of reaction temperature, catalyst loading, cross-linking density, and gel particle size on the transient and steady-state behavior of the cartridge flow reactor through an automated flow chemistry platform. The PMHS-supported catalytic particles demonstrate minimal deactivation and leaching over a continuous (80 h) Suzuki–Miyaura cross-coupling reaction at a 30 min nominal residence time at a relatively high reaction temperature of 95 °C. The developed modular flow chemistry strategy equipped with the cartridge flow reactor enables accelerated studies of the fundamental and applied characteristics of gel-supported catalysts while providing increased safety, higher throughput, and removal of the separation step needed for catalyst recovery compared to homogeneous cross-coupling reactions in batch reactors.