We investigate the effects of large predeformation on the propagation of planar solitary waves in flexible mechanical metamaterials comprising an array of hinged rotating squares. The predictive framework of our theoretical analysis shows that the predeformation can be exploited to control the characteristics of the supported elastic vector solitons via the tuning of the metamaterial dispersive and nonlinear properties. Together with numerical tests, our study provides a better understanding of the tunable dynamic response of flexible nonlinear mechanical metamaterials and explores more advanced configurations and effects that could open avenues for the design of systems with enhanced tunability.