UAV689, please see my post above and pray tell what you think!
You could fly a constant heading with reference to magnetic north (this is assuming you are referencing magnetic, and no means to true), but this wouldn't give you a parallel of latitude, even at 090 or 270, because it is referenced to magnetic north, not true.
For example, this is why we have magnetic variation, which applies to ALL headings. This same value also varies geographically, so the error is induced both longitudinally and laterally.