Flexoelectricity is defined as the higher-order electromechanical coupling due to the interplay between strain gradients and the electric field. Flexoelectricity hinges on strain gradients, which makes it a size-dependent phenomenon. Thus, flexoelectricity is very prominent at smaller scales, with intense applications to high-precision micro- and nano-electromechanical systems such as sensors, actuators, energy harvesters, etc. Flexoelectricity in linear dielectrics [1] and piezoelectrics [2] is well analyzed. However, flexoelectricity in ferroelectric materials is still not explored. In the current work, a non-linear ferroelectric material model is successfully incorporated into the flexoelectric framework. To achieve this, a three-dimensional mixed FE is extensively extended with the non-linear micromechanical ferroelectric material model based on [3]. This involves consideration of the influence of strain gradient effects on the ferroelectric domains. First, mixed~FE implementation for flexoelectricity is checked against the analytical solution in a simple case of dielectric solids. Simultaneously, an extended micromechanical ferroelectric switching model is tested on the single- and poly-crystalline representative volume elements. Following this, novel simulations of ferroelectric structures, e.g. truncated pyramid, including higher-order electromechanical coupling effects are performed for the first time. It is observed that a strong asymmetry is manifested in the strain vs. electric field plot, commonly known as the butterfly loop. The degree of asymmetry increases with an increase of the flexoelectric coefficient. The successful implementation of the research on the combined effect of nonlinear ferroelectric behavior including higher-order gradient terms significantly broadens the horizon of understanding smart structures behavior at small scales. [1] K. Tannhäuser, P.H. Serrao and S. Kozinov, A 3D collocation FEM for higher-order electromechanical coupling. Comput. Struct., Vol. 291, pp. 107219, 2024. [2] P.H. Serrao and S. Kozinov, Robust mixed FE for analyses of higher-order electromechanical coupling in piezoelectric solids. Comput Mech., 2023. [3] J. Huber, N.A. Fleck, C.M. Landis and R.M. McMeeking, A constitutive model for ferroelectric polycrystals. J. Mech. Phys. Solids, Vol. 47, pp. 1663–1697, 1999.