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In this study, a coupled computational fluid dynamics and discrete element method (CFD-DEM) model is constructed to deal with the motion of flexible fibers in molten thermoplastic during fused deposition modeling (FDM) 3D printing process. The effects of fiber stiffness and length on fiber bridging and nozzle clogging are investigated. Numerical results show that fiber deformation has a clear influence on nozzle clogging even when the fibers are as short as 0.24 mm for the printing of short carbon fiber reinforced polyamide-6 (sCF/PA6) composite with a fiber volume fraction of 13.34%. Through a particle-scale analysis on the fiber architecture in terms of coordinate number, contact force, and fiber orientation, the influence of fiber deformation is identified. It is found that the flexible fibers are more sensitive to the geometry and profile changes of the nozzle internal walls, which leads to a larger inclination of the flexible fiber in the nozzle. Complex interlocking structures are formed by flexible fibers in the printer nozzle, promoting the fiber bridges. The results of this paper provide insights for the development and optimization of printer nozzles to enable the printing of longer fibers without potential nozzle clogging.