  For any flag nestohedron, we define a flag simplicial complex whose
$f$-vector is the $\gamma$-vector of the nestohedron. This proves that the
$\gamma$-vector of any flag nestohedron satisfies the Frankl-F\"{u}redi-Kalai
inequalities, partially solving a conjecture by Nevo and Petersen \cite{np}. We
also compare these complexes to those defined by Nevo and Petersen in \cite{np}
for particular flag nestohedra.
