Proof with auto.
induction l...
simpl.
intros.
rewrite IHl...
rewrite H...
Qed.
Hint Resolve Permutation_concat.

Lemma Permutation_concat_map_app T A (f g: A -> list T) l:
Permutation (concat (map (fun x => f x ++ g x) l)) (concat (map f l ++ map g l)).