The stabilizing effect of a sheared axial flow is investigated in the ZaP flow Z-pinch experiment at the University of Washington. Long-lived, hydrogen Z-pinch plasmas are generated that are 1 m long with an approximately 10 mm radius and exhibit gross stability for many Alfvén transit times. Large magnetic fluctuations occur during pinch assembly, after which the amplitude and frequency of the fluctuations diminish. This stable behaviour continues for an extended quiescent period. At the end of the quiescent period, fluctuation levels increase in magnitude and frequency. Axial flow profiles are determined by measuring the Doppler shift of plasma impurity lines using a 20-chord spectrometer. Experimental measurements show a sheared flow that is coincident with low magnetic fluctuations during the quiescent period. The experimental flow shear exceeds the theoretical threshold during the quiescent period, and the flow shear is lower than the theoretical threshold at other times. The observed plasma behaviour and correlation between the sheared flow and stability persists as the amount of injected neutral gas and experimental geometry are varied. Computer simulations using experimentally observed plasma profiles show a consistent sheared flow stabilization effect. Plasma pinch parameters are measured independently to demonstrate an equilibrium consistent with radial force balance.