A cellular automata-multiple relaxation time lattice Boltzmann three-dimensional coupled model with a dynamic grid has been developed for the objective of simulating the kinematic growth process of binary alloy dendrites. In this model, the cellular automata approach is applied to calculate the dendrite growth, and the multiple relaxation time lattice Boltzmann approach is utilized to emulate the melt flow. Furthermore, a dynamic grid scheme with one level of refinement in comparison to the global grid is proposed as a means of addressing the issue of dendrite motion with the sharp interface. This approach is intended to reduce the considerable memory requirements associated with three-dimensional simulations, while also facilitating acceleration through the use of a graphics processing unit. Lastly, the constructed model was utilized to emulate the translational, rotational and free settling processes of a three-dimensional individual dendrite within laminar, shear and natural convection flows, as well as the settling of multiple dendrites, respectively. The findings of the simulation indicate that the growth of the dendrites in solid solution alloys is predominantly influenced by the local solute composition. Moreover, the impact of dendrite movement on its growth rate is primarily associated with the relative velocity of the dendrite and the melt.