The incompatibility between inorganic flame retardants and organic acrylic coatings represents a significant challenge that requires resolution. This work selected environmentally friendly organic aqueous acrylic coatings as the substrate, sodium silicate hydrate as the inorganic flame retardant, and melamine cyanurate (MCA) as the flame-retardant modifier and the flame-retardant co-modifier, with the objective of improving the dispersion and flame-retardant properties of sodium silicate hydrate in the aqueous acrylic coatings. Subsequently, the sodium silicate/MCA/waterborne acrylic acid flame-retardant coating was prepared. The flame-retardant treatment was then applied to poplar veneer in order to create a flame-retardant poplar veneer. The dispersion of the flame-retardant coating was characterized by scanning electron microscopy (SEM), energy-dispersive spectroscopy (EDX), and X-ray diffractometry (XRD). Furthermore, the flame-retardant properties of the flame-retardant poplar veneer were analyzed by thermogravimetry (TG), limiting oxygen index (LOI), and cone calorimeter. The results demonstrated that the MCA-modified sodium silicate flame retardant was well dispersed in aqueous acrylic coatings. The results of the flame-retardant properties of the poplar veneer indicated that the ignition time of the 9% flame retardant-treated poplar veneer was increased by 122.7%, the limiting oxygen index value was increased by 43.0%, and the peak heat release rate (pHRR), the peak total heat release rate (pTHR), and the peak mass loss rate were decreased by 19.9%, 10.8%, and 27.2%, respectively, in comparison to the non-flame retardant-treated poplar veneer. Furthermore, the residual char mass increased by 14.4%, and the residual char exhibited enhanced thickness, density, and regularity. The results demonstrated that MCA was an effective promoter of sodium silicate dispersion in acrylic coatings. Furthermore, the sodium silicate/MCA/waterborne acrylic flame-retardant coating significantly enhance the flame retardancy of wood, and its flame retardant mechanism was consistent with the synergistic silicone–nitrogen expansion flame-retardant mechanism. This work presents a novel approach to enhancing the dispersion of inorganic flame retardants in organic coatings, offering a valuable contribution to the advancement of research and application in the domains of innovative flame retardant coatings and flame retardant wood.