A new secure key distribution scheme based on the dynamic chaos synchronization of two cascaded semiconductor laser systems (CSLSs) subject to common chaotic injection and random phase-modulated optical feedback is demonstrated. In this scheme, Alice and Bob adopt two independent random sequences to control the phase modulators of CSLSs, which induces a dynamic perturbation to the chaos synchronization. We thoroughly investigate the chaos synchronization performance under different phase-shift conditions with cross-correlation function, and systematically discuss the feasibility and security of the system. The results show that, with proper injection and feedback strength, the correlation coefficient gap between phase shift match and mismatch is clear and robust to the parameter mismatches in the CSLSs and those between the two CSLSs. Based on this, high-quality key distribution can be performed by picking out the identical random bits from the two independent random sequences according to the computational correlation. Moreover, the investigations on the information theoretic security and rate of the key distribution show that the security of the key distribution scheme can be further enhanced by properly increasing the number of layers in the CSLSs or employing high-order modulation format.