Polyelectrolyte spin assembly (PSA) of multilayers is a sequential process featuring adsorption of oppositely charged polyelectrolytes from dilute solutions undergoing spin-coating flow. Here, we report on the dependence of PSA multilayer buildup of poly(sodium 4-styrenesulfonate) and poly(allylamine hydrochloride) on solution ionic strength and spin speed. We observed that at a given spin speed, the PSA coating growth rate (thickness/bilayer) and polymer surface coverage shows a nonmonotonic dependence on salt concentration, first increasing and then decreasing with increasing solution ionic strength. This is argued to be a manifestation of two competing mechanisms responsible for the layer formation. At low salt concentrations, the electrostatic interactions control the multilayer assembly process, while at high salt concentrations it is dominated by shear flow. We explain this nonmonotonic behavior in the framework of a Flory-like theory of multilayer formation from polyelectrolyte solution under shear flow. Additionally, the PSA process led to multilayer coatings with a radial dependence on thickness at lower spin speed in the shear-dominated regime. On increasing spin speed, such radial dependence subsided, eventually leading to uniform coatings by planarization. The surface topography of the multilayered coatings adsorbed at salt concentration less than 0.1 M was flat and featureless for all studied spin speeds. Unique morphological features in the films were formed at salt concentration higher than 0.1 M, the size of which depended on the spin speed and solution ionic strength.