Why does Gene say that Finny wouldn't be good in a war?

Gene knows that Finny does not have the soldier's mentality; that is, he doesn't have enough malice within him to kill others on behalf of a cause. Finny's main concern is that everyone be treated equally, and he plays the part of the peacemaker within the story itself. War, obviously, is the opposite of peace, and therefore Finny would be a poor candidate for any type of military duty.

This is what Gene means when he states what he does about Phineas "(not being) any good in the war even if nothing had happened to your leg." It isn't intended as an insult; it's simply a statement of truth.