Flexible materials with both in-plane and out-of-plane piezoelectric coefficients are needed in the development of advanced nanoelectromechanical systems. However, the challenge is to find flexible materials with the coexistence of in-plane and -out-of-plane piezoelectric responses, which hinders the progress of high-performance piezoelectric sensor development. In this paper, we propose the flexible XMAY2 (X = I; M = Ti, Zr; A = Al, Ga; Y = S, Se) monolayers, which belong to the group III-VI XMAY2 family, which showcase notable in-plane and out-of-plane piezoelectric coefficients. The in-plane (d11) and out-of-plane (d31) piezoelectric coefficients of the XMAY2 monolayers vary from 5.20 to 7.04 pm/V and from −0.23 to 0.48 pm/V, respectively. The large in-plane and out-plane piezoelectric responses coexist (d11 = 7.04 pm/V; d31 = 0.48 pm/V) in the IZrGaS2 monolayer, which is larger than other materials in the XMAY2 family, such as SMoSiN2 (d11 = 2.51; d31 = 0.28 pm/V). In addition, the mechanical and transport properties of XMAY2 demonstrate its impressive flexibility characteristics as well as its efficient electrical conductivity. Due to inversion symmetry breaking in both atomic structure and charge distribution of XMAY2 monolayers, the group III-VI XMAY2 family exhibits a potentially rich scope of applications in the field of piezoelectricity.