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

$$\forall x\:\bigl(x\in s\leftrightarrow\exists y\:\bigl(\forall t\:(t\in y\leftrightarrow t\in x)\land y\notin x\bigr)\bigr).$$
If $s\in s$, then there is an $S$ with the same members as $s$ such that $S\notin s$.

But if $S\notin s$, then for all $T$ with the same members as $S$, $T\in S$. In particular $S\in S$ and thus $S\in s$.

If $s\notin s$, then for all $S$ with the same members as $s$, $S\in s$. In particular $s\in s$.