The electrolysis of water is one of low-cost green hydrogen production technologies. The main challenge regarding this technology is designing and developing low-cost and high-activity catalysts. Herein, we present a strategy to fabricate flexible electrocatalysts based on nickel–iron (NiFe) alloy coatings. NiFe coatings were plated on the flexible copper-coated polyimide surface (Cu/PI) using the low-cost and straightforward electroless metal-plating method, with morpholine borane as a reducing agent. It was found that Ni90Fe10, Ni80Fe20, Ni60Fe40, and Ni30Fe70 coatings were deposited on the Cu/PI surface; then, the concentration of Fe2+ in the plating solution was 0.5, 1, 5, and 10 mM, respectively. The morphology, structure, and composition of NixFey/Cu/PI catalysts have been examined using scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDX), X-ray diffraction (XRD), and inductively coupled plasma–optical emission spectroscopy (ICP-OES), whereas their activity has been investigated for hydrogen evolution (HER) and oxygen evolution (OER) reactions in 1 M KOH using linear sweep voltammetry (LSVs). It was found that the Ni80Fe20/Cu/PI catalyst exhibited the lowest overpotential value of −202.7 mV for the HER, obtaining a current density of 10 mA cm−2 compared to Ni90Fe10/Cu/PI (−211.9 mV), Ni60Fe40/Cu/PI (−276.3 mV), Ni30Fe70/Cu/PI (−278.4 mV), and Ni (−303.4 mV). On the other hand, the lowest OER overpotential (344.7 mV) was observed for the Ni60Fe40/Cu/PI catalyst, obtaining a current density of 10 mA cm−2 compared to the Ni35Fe65 (369.9 mV), Ni80Fe20 (450.2 mV), and Ni90Fe10 (454.2 mV) coatings, and Ni (532.1 mV). The developed Ni60Fe40/Cu/PI catalyst exhibit a cell potential of 1.85 V at 10 mA cm−2. The obtained catalysts seem to be suitable flexible catalysts for HER and OER in alkaline media.