I know that polystyrene nanoparticles exhibit a mild negative charge in various solutions determined by zeta potential measurements. However, does this change when the material is now flat on a spin coated surface such as a coverslip?
All materials exhibit some form of surface charge. In the case of a film such as this is can be caused by a variety of effects - surface groups (e.g. carboxylate) in air, chemisorption induced segregation for mixtures and so on. In solution, as you correctly state, the chemistry of the material and the external conditions (e.g. pH) affect the zeta potential which is a measure of how particles interact in colloidal suspension. In suspension the magnitude of the surface charge can be measured directly e.g. see attached.