The US flag always is to be on "it's own right." If on a platform it should be on the speakers right, if it is on the floor it should be on the congregation's right. No "law" so speak here, simply a code of practice.
Saying that, I really don't know what US churches uniquely developed the practice of have a national flag in church. It would be interesting to find out why. I personally have never been in a church outside the US that displayed the national flag.
C4K is correct on a "flag code".
A private entity (yes, that includes a church) may display the flag, as he, she, or it/they deem appropriate.
Here is a listing of some common flag 'suggestions' codes and questions.
Personally, I have seen the American flag and the Christian flag displayed on both sides of our local church auditorium, over time.
I never got particularly interested in which exact position was technically correct, and frankly would be far more concerned about intentional disrespect to these flags, because of what they symbolize, than about exact proper ettiquette by any, including me, who do not know all the exact details of proper ettiquette and customs.
Our church has decided that the American flag should not be displayed outside our church, however it is displayed inside our church, the pledge of allegiance is said in our AWANA Club Meetings, but I cannot understand this, our religious freedoms are due to those who died defending these rights, the American flag was always displayed at my church when I was a child, why do we honor veterans and sing their praises in church but refuse to display it outside our churches, if we cannot display the flag of our country outside we should not sing it’s praises inside the church, I’m now looking for a church that is not hiding patriotism behind closed doors trying to not offend the left wingers of this world
I see no reason for an American flag to be posted inside or outside a church. A civil religion ill-becomes Baptists. If you want it, fine. But I can't see that it adds anything to true religion.