Hello Wes -- welcome aboard!
The civilian flag code does not deal with details like this, so the best reference is probably military regulations. I'll use the Army as a suitable example. The relevant reference is Field Manual FM 3-21.5, Honors and Ceremonies. The Air Force equivalent (AFMAN 36-2203) is similiar.
The FM is quite detailed, but I'll try to summarize the main ideas. There are two basic positions for the US flag, "carry" and "order." The FM defines them as follows:
"At the Carry, rest the ferrule of the staff in the socket of the sling. The socket is below the waist and adjusted to ensure that the finials of all Colors are of equal height . . . Grasp the staff with the right hand (even with the mouth) and incline it slightly to the front with the left hand securing the ferrule in the socket. The left hand may be positioned immediately below the right hand to more firmly secure the Colors on windy days."
"At the Order, rest the ferrule of the staff on the marching surface touching the outside of the right footgear opposite the ball of the right foot. Hold the staff in the right hand with the back of the hand facing outward and the fingers wrapped around the staff. Rest the staff against the hollow of the shoulder."
Your question, I think, deals with the correct position of the national flag in a stationary formation (as opposed to marching). As I interpret the FM, the colors should be in the order position except when the formation is saluting by "present arms." The FM says: "When the Colors salute with troops who execute Present Arms from the Order, the Color bearers assume the position of Carry at the command ARMS and then execute the Color Salute." If one of the service flags, or a unit color, is carried along with the national color, the bearer of the unit color executes the salute as follows: "This position is assumed from the carry by slipping the right hand upward about 4 inches and then thrusting the arm forward shoulder high and horizontal to the marching surface forming an approximate 45-degree angle." Note that this applies only to organizational colors; the national flag is never dipped in salute (on land, anyway).
I hope this addresses your question -- if not, let us know!