Thanks to their excellent properties of low cost, lightweight, portability, and conformity, flexible perovskite-based tandem solar cells show great potentials for energy harvesting applications, with flexible perovskite/c-silicon tandem solar cells particularly promising for achieving high efficiency. However, performance of flexible perovskite/c-silicon monolithic tandem solar cells still greatly lags, due to challenges in simultaneously achieving both efficient photocarrier transport and reliable mitigation of residual stress. Here, we reveal the critical role of perovskite phase homogeneity, for achieving highly-efficient and mechanical-stable flexible perovskite/c-silicon heterojunction monolithic tandem solar cells (PSTs) with textured surface. Through ensuring high phase homogeneity, which promotes charge transfer across all facets of the pyramid on the textured substrates and releases the residual stress at the perovskite/c-silicon interface, we demonstrate flexible PSTs with a bending curvature of 0.44 cm, and a certified power conversion efficiency of 29.88% (steady-state 29.2%, 1.04 cm aperture area), surpassing all other types of flexible perovskite-based photovoltaic devices. Our results can lead to broad applications and commercialization of flexible perovskite/c-silicon tandem photovoltaics.