We study the correlation between chemical composition and vortex dynamics in Ni-doped CaK(Fe1−xNix)4As4 (x=0, 0.015, 0.025, 0.03, and 0.05) single crystals by performing measurements of the critical current densities Jc and the flux creep rates S. The magnetic relaxation of all the crystals is well described by the collective creep theory. The samples display a glassy exponent mu within the predictions for vortex bundles in a weak pinning scenario and relatively small characteristic pinning energy (U0<100K). The undoped crystals display modest Jc values at low temperatures and high magnetic fields applied along the c axis. Jc(T) dependences at high fields display an unusual peak. The enhancement in Jc(T) matches with an increase in U0 and the appearance of a second peak in the magnetization. As Ni doping increases, whereas there is a monotonic decrease in Tc there is a nonmonotonic change in Jc. Initially Jc increases, reaching a maximum value for x=0.015, and then Jc decreases for x >=0.025. This change in Jc(x) is coincident with the onset of antiferromagnetic order. The magnetic field dependence of Jc(H) also manifests a change in behavior between these x values. The analysis of the vortex dynamics for small and intermediate magnetic fields shows a gradual evolution in the glassy exponent mu with Ni content, x. This implies that there is no appreciable change in the mechanism that determines the vortex relaxation.