) Flakes*

We present evidence of thickness dependent superconducting behavior in strain-free Fe(Te_0.7Se_0.3) flakes. Due to non-uniform Te/Se spatial distribution, we find that R(T) behavior in flakes <10nm can be explained and confirmed using the BKT transition for inhomogeneity model, as well as finite state effects(FSE). For >10nm flakes we find a systematic suppression of the superconductivity and broadening of the superconducting phase transition. Additionally, we present a self-heating model at the metal-superconductor-metal(MSM) interface to explain unusual observed switching behavior in I-V characteristicsfor flakes thinner than 10nm. We propose a 2D network of superconducting paths connecting superconducting islands within Fe(Te_0.7Se_0.3) thin flakes to describe the thickness-dependent behavior of this natural percolating system.