Flexibly Stratified Comprehension is inconsistent. By Flexibly Stratified Comprehension, there is an s such that

 ∀x(xεs<-->∃y(∀t(tεy<-->tεx))∧y∉x). If sεs, then there is an S with the same members as s such that S∉s.

 But if S∉s, then for all T with the same members as S, TεS. In particular SεS snd thus Sεs.

If s∉s, then for all S with the same members as s, Sεs. In particular sεs.