Future Flexible HVDC Transmission Systems will consist of several active and passive infrastructures including DC Power Flow Controller (DC-PFC) device. The addition of the DC-PFC to the future Multi-Terminal HVDC (MT-HVDC) grids arises some key concerns such as stability, system interoperability, and possible adverse interactions. Hence, a suitable model is necessary to conduct deep frequency domain analysis. In this context, this paper proposes a linearized model for small-signal stability analysis of flexible MT-HVDC grids in state space framework that can be straightforwardly utilized in the process of control design. In this paper, a spick-and-span, systematic and step-by-step process to derive the small signal model of all flexible MT-HVDC grid components is presented such that each sub-system is modeled individually and then all are integrated together. The derived model is cross-verified by time domain simulations of a nonlinear system model in a MATLAB/SIMULINK platform for CIGRE DCS3 MT-HVDC test grid.