Let A be a Banach algebra and φ be a character on A. In this paper, we give a necessary condition, called condition (W ), for φ-biflatness of Banach algebra A as well as some hereditary properties. We also study the relation between left φ-amenability and condition (W ). Moreover, we apply these results and characterize the φ-biflatness of abstract symmetric Segal algebras. In particular, we identify φ-biflatness of the Lebesgue-Fourier algebra LA(G), where G is a unimodular locally compact group. These results describe a homological property for Segal algebras in the setting of biflatness based on character φ.