  We prove that the initial degenerations of the flag variety admit closed
immersions into finite inverse limits of flag matroid strata, where the
diagrams are derived from matroidal subdivisions of a suitable flag matroid
polytope. As an application, we prove that the initial degenerations of
$\operatorname{F\ell}^{\circ}(n)$ -- the open subvariety of the complete flag
variety $\operatorname{F\ell}(n)$ consisting of flags in general position --
are smooth and irreducible when $n\leq 4$. We also study the Chow quotient of
$\operatorname{F\ell}(n)$ by the diagonal torus of $\operatorname{PGL}(n)$, and
show that, for $n=4$, this is a log crepant resolution of its log canonical
model.
