Electromechanical phenomena in two-dimensional (2D) materials can be related to sizable electric polarizations and switchable spontaneous ferroelasticity, allowing them to be used as miniaturized electronic and memory devices. Even in a parent centrosymmetric (nonpolar) ferroelastic (FE) material, non-zero polarization can be produced around the FE domain wall, owing to the strain-gradient-induced flexoelectricity. Compared with the negligibly weak flexoelectric effect in bulk compounds, significant electric polarizations can be expected in 2D FE materials that sustain a large elastic strain and a strain gradient. Using first-principles calculations, we predict that spontaneous 2D ferroelasticity and domain-wall flexoelectricity can be simultaneously realized in synthetic HgX2 (X = Br or I) monolayers. The FE phase renders three oriented variants, which form FE domain walls with a large strain gradient and the associated domain-wall flexoelectric polarizations. Our thermodynamic stability analysis and kinetic barrier simulations allow us to manipulate the domain-wall flexoelectricity via applied mechanical stress, thereby enabling future electromechanical applications in nanoelectronics.