To investigate the effect and ability of FACTS devices using the Fast and Flexible Holomorphic Embedding technique (FFHE), it is necessary to develop an embedded system for these devices. Therefore, this paper presents FFHE based embedded system for STATCOM and UPFC. The embedded system is also proposed for their controlling modes. The introduced embedded system for STATCOM and UPFC is flexible which allows to take any state as an initial guess instead of fixed state, which leads towards the reduced runtime and decreases the required number of terms, as compared to the standard Holomorphic Embedded Load-Flow method (HELM). To demonstrate the effectiveness and practicability, the proposed models of STATCOM and UPFC have been tested for several cases. Further, the developed recursive formulas for power balance equations, devices' physical constraints, and their controlling modes are thoroughly investigated and examined. From several tests, it is found that the proposed embedded system requires less execution time and reduces the error at higher rate.