Flame-retarded polymers, such as polyester textiles and sheets, are attracting attention with regard to their sustainability. Mechanical recycling is currently the most frequently used technique for improving the circularity of plastics. However, one complication of mechanical recycling is associated with the (still) inevitable mixtures of polymers and additives, which can influence material stability and significantly deteriorate the mechanical properties of recycled products. In this study, we aim to specifically investigate the interactions between mixtures of phosphorus flame retardants (FRs) in polyethylene terephthalate (PET) and evaluate their potential role in the mechanical recycling of melt-spun fibers. Two highly relevant commercial FRs, namely a DOPO-derivative (DOPO-PEPA or DP) and Aflammit PCO 900 (AF), are added to PET compounds as additives using a melt compounder. The melt stability of PET/FR compounds over extended processing time is assessed by chemical, thermal, and rheological measurements. DP shows a molecular lubrication effect, lowering the melt viscosity of PET, while AF promotes chemical changes (i.e., chain branching/crosslinking). Interestingly, a PET compound containing hybrid mixtures of DP/AF 20/80 (wt%/wt%) shows the most stable behavior at high temperatures under both nitrogen and air atmospheres, thus showing a synergistic effect. Most importantly, in a recycling scenario, the stabilization effect persists at diluted concentrations below the typical FR contents in PET. Multiple extrusion cycles are used to assess the repeated processing behavior of the compounds, and the mechanical properties and fire behavior of melt-spun fibers are compared before and after recycling. The results reveal that DP can maintain the mechanical performance of recycled PET/FR fibers, even if it is mixed (contaminated) with AF.