Helical hierarchy found in biomolecules like cellulose, chitin, and collagen underpins the remarkable mechanical strength and vibrant colors observed in living organisms. This study advances the integration of helical/chiral assembly and 3D printing technology, providing precise spatial control over chiral nano/microstructures of rod-shaped colloidal nanoparticles in intricate geometries. We designed reactive chiral inks based on cellulose nanocrystal (CNC) suspensions and acrylamide monomers, enabling the chiral assembly at nano/microscale, beyond the resolution seen in printed materials. We employed a range of complementary techniques including Orthogonal Superposition rheometry and in situ rheo-optic measurements under steady shear rate conditions. These techniques help us to understand the nature of the nonlinear flow behavior of the chiral inks, and directly probe the flow-induced microstructural dynamics and phase transitions at constant shear rates, as well as their post-flow relaxation. Furthermore, we analyzed the photo-curing process to identify key parameters affecting gelation kinetics and structural integrity of the printed object within the supporting bath. These insights into the interplay between the chiral inks self-assembly dynamics, 3D printing flow kinematics and photo-polymerization kinetics provide a roadmap to direct the out-of-equilibrium arrangement of CNC particles in the 3D printed filaments, ranging from uniform nematic to 3D concentric chiral structures with controlled pitch length, as well as random orientation of chiral domains. Our biomimetic approach can pave the way for the creation of materials with superior mechanical properties or programable photonic responses that arise from 3D nano/microstructure and can be translated into larger scale 3D printed designs.