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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-Kalaiinequalities, partially solving a conjecture by Nevo and Petersen \cite{np}. Wealso compare these complexes to those defined by Nevo and Petersen in \cite{np}for particular flag nestohedra.

Frankl-F\"{u}redi-Kalai Inequalities on the $\gamma$-vectors of flag nestohedra