"We don’t have to prove that God exists to the professing atheist."
Technically, you don't have to breathe either. I mean, it is a choice.
"This is because he intuitively knows that He exists."
Please don't presume to tell me what I do or do not know. That's the height of arrogance.
"Every person has a God-given conscience."
No. Many people have a conscience, but we are back to your proving God exists before you can claim that conscience is God-given.
Also, many sociopaths don't have a conscience.
"The Bible tells us that this is the 'work of the law written on their hearts.'"
But, as much of the Bible is patently wrong, no one should assume that such unvarifiable claims in the Bible are true.
"Just as every sane person human being knows that it’s wrong to lie, steal, kill and commit adultery, he knows that God should be first in his life."
Absolutely correct, except for that claim about God.
Your agrument for the existence of God seems to be only that you believe in God therefore everyone knows God exists. That's not flawed logic, it's devoid of logic.
