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In this study, we present multiplexed anodic stripping voltammetry (ASV) detection of heavy metal ions (HMIs)—As(III), Cd(II), and Pb(II)—using a homemade electrochemical cell consisting of dual working, reference and counter screen-printed electrodes (SPE) on polyimide substrate integrated with a 3D-printed flow cell. Working and counter electrodes were fabricated by the screen-printing of graphite paste while the Ag/AgCl paste was screen-printed as a reference electrode (Ag/AgCl quasi-reference electrode). The working electrodes were modified with (BiO)2CO3-reduced graphene oxide (rGO)-Nafion [(BiO)2CO3-rGO-Nafion] and Fe3O4 magnetic nanoparticles (Fe3O4MNPs) decorated Au nanoparticles (AuNPs)-ionic liquid (IL) (Fe3O4-Au-IL) nanocomposites separately to enhance HMIs sensing. Electrochemical detection was achieved using square wave ASV technique. The desired structure of the flow electrochemical cell was optimized by the computational fluid dynamic (CFD). Different experimental parameters for stripping analysis of HMIs were optimized including deposition time, deposition potential and flow rate. The linear range of calibration curves with the sensing nanocomposites modified SPE for the three metal ions was from 0–50 μg/L. The limits of detection (S/N = 3) were estimated to be 2.4 μg/L for As(III), 1.2 μg/L for Pb(II) and 0.8 μg/L for Cd(II). Furthermore, the homemade flow anodic stripping sensor platform was used to detect HMIs in simulated river water with a 95–101% recovery, indicating high selectivity and accuracy and great potential for applicability even in complex matrices.