This study explores the influence of triphenylphosphine oxide (TPPO) as a flame-retardant (FR) additive on the crystallinity, mechanical performance, and flame retardancy of polylactic acid (PLA) bicomponent fibers. Although TPPO has been investigated in other polymer systems, its application in PLA-based FR fibers has rarely been reported. To address both processability and end-use performance, this study focuses on understanding the rheological behavior of FR-embedded PLA compounds and improving the mechanical and FR properties of the final fiber products. Rheological analyses at various temperatures revealed that TPPO incorporation increased melt viscosity, exhibiting a rheological percolation threshold at 4 wt%, which induced pseudo-network formation. Thermal analyses using differential scanning calorimetry and dynamic mechanical analysis showed that increasing TPPO content reduced crystallinity and lowered both the glass transition and melting temperatures. Bicomponent PLA fibers with a sheath-core structure were fabricated and exhibited enhanced flame retardancy, achieving a limiting oxygen index (LOI) of up to 37.8% at 8 wt% TPPO. Although a slight decline in mechanical properties was observed, fibers containing 6–8 wt% TPPO maintained acceptable tensile strength (3.76–3.81 gf denier−1) and elongation (24.06%–24.50%). These results demonstrate that TPPO, a previously underexplored additive in the PLA system, is an effective additive in producing FR and sustainable fibers for textile and polymer-based applications.