Direct ink writing is a versatile tool that is capable of printing thermoset resins in large format parts. Although there are many advantages to DIW, there are significant hurdles to overcome regarding the ideal resin rheology to ensure successful printing and good mechanical performance. Determining the optimum flow behavior of 3D printing fluids is extremely important to determine the final products' internal structure and performance. It has been shown that the shape and properties of the filament during the printing process are highly affected by the shear-thinning behavior and spreading of fluids. For instance, if the viscosity is too low or wettability is high, the resin spreads quickly; making it difficult to print the resin using DIW. On the other hand, if the viscosity is too high or wettability is low, printed filaments have poor cohesive strength and the mechanical properties of the part are low. In this work, we use rheology to investigate the correlation between shear thinning behavior and the spreading of filaments for model photocurable thermoset resin, denoted as DA2, which is doped with fumed silica to modify the rheology. The shear thinning behavior is directly correlated to the amount of silica additive, and the spreading during printing was observed to follow a power-law behavior with time. We find that spreading of filament is increased with increasing infill rate due to the shear thinning behavior of the resin.