Antibacterial powder coatings have attracted increasing attention with the awakening of people’s health awareness. Silver antibacterial agent has been widely used in coating system due to its superior stability and durability. However, silver ions have the problems of excessive release rate and the tendency to cause yellowing of the coating film. The addition of Cu2+ and Zn2+ can effectively alleviate these two phenomena. In this paper, the ternary exchange kinetics of Ag+, Cu2+, and Zn2+ were studied to provide a theoretical basis for the synthesis of LTA-Ag-Cu-Zn. The reaction kinetics study shows that the selectivity and the adsorption capacity of LTA to Ag+ is higher than that of Cu2+ and Zn2+. The thermodynamic analysis discovers that LTA has the highest selectivity for Ag+, and the exchange between the two is spontaneous. In contrast, the selectivity of LTA to Cu2+ and Zn2+ is concentration-dependent. By establishing the three-ion competitive adsorption curve, it is found that the selectivity of Ag+ is the highest, and the selectivity of copper and zinc is similar. These trends result from Ag+ ions’ low hydration energy, small hydration radius, and strong electronegativity. This research lays the groundwork for developing high-performance LTA-Ag-Cu-Zn tri-ion exchange antibacterial agents.