Does a wife need to get the permission of her husband if she wishes to give someone Zakāh from his money ?

If the husband has given some money to his wife, then she has become the owner of that money, and there is no need to seek permission from him. Of course! If she is keeping his money as a trust (amānah), then she must ask her husband about wherever she intends spending it whether on Zakāh or on something else.