Yes, they flow from God. But morals are defined as "conforming to a standard of right behavior". That "standard" is set by religious teachings.
And where do the "standards of right behavior come from" - God. Men are the teachers of religious teachings and, unless those teachings confirm to absolute moral principles from God, then the only remaining option is that the teachings are RELATIVE TO THE TEACHER, or to men, which would make religious teachings tantamount ot moral relativism. Morals have only two possible sources - man or God - that exhausts the choices.
Religious teachings in Christianity come from the Bible which contains the moral absolutes that come from God.