This paper proposes an integrated centralized multiperiod planning framework for local flexibility markets (LFMs) in unbalanced distribution networks (UDNs). It co-optimizes line reinforcement and phase-aware flexibility procurement subject to unbalanced three-phase AC power-flow constraints using a rectangular-coordinate branch current-voltage representation. The resulting MBQCQP captures AC bilinearities and investment-dependent network constraints. For each fixed investment vector, the model is reformulated as a bounded nonconvex QCQP and lifted into a completely-positive-programming-based (CPP-based) representation, from which semidefinite programming (SDP) and SDP-Moment relaxations are derived. Numerical results on a modified IEEE 13-node feeder show that generationside flexibility reduces reinforcement costs by 22.86% relative to the no-flexibility case, while the combined use of local load- and generation-side flexibility fully eliminates reinforcement investment. The SDP-Moment relaxation closes the gap in all tested cases and recovers the exact investment decisions, demonstrating that strengthened lifted relaxations can provide reliable bounds for phase-aware investment planning in UDNs.