Is that a nondenominational flag? Or one for a particular sect? I can easy spot The Catholic Flag, but I am not familiar with those of other sects.
The Catholic Flag is actually the State Flag of the Vatican.
and for that rules applied to other National Flags apply.
- If the flags of other nations are displayed with the American Flag, they should be of equal size and at equal heights on separate staffs at a time of peace. The American Flag should be displayed to the (flag's own) right but not higher than other national flags.
And I think I know where Sea got the whole church flag higher than the US flag thing. It's for a specific case when a Naval Chaplain is giving a service on a ship, Presumably to let the people know what ship he's doing the service on.
- A church pennant may be flown above the American Flag if a church service is done by naval chaplains at sea for personnel of the Navy. After the service is over, the American Flag must again be placed in the prominent position.
Displaying the Flag with other Flags