We report experimental and theoretical results on the flexoelectric instability and crossover between flexoelectric domains and electroconvection in a hybrid aligned nematic MBBA under d.c. voltage. At threshold a spatially periodic flexoelectric deformation in the form of longitudinal domains (along the planar director) was observed. With increasing voltage the director deviation out of the initial plane becomes clearly detectable. Observations of tracers show that hydrodynamic flow develops inside the flexoelectric stripe pattern in the form of circular orbits perpendicular to the domain stripes. With further increasing d.c. voltage electroconvection sets in in the form of drifting oblique rolls inside the flexoelectric domains.