A B767-300 encountered a split flap condition on arrival. They performed a go-around and appropriate checklists followed by a safe landing.

Narrative

Whilst configuring for landing; we experienced a 'split flap indication' at 15/20 degrees respectively. We returned the flaps to an equal setting at 15 degrees; executed a missed approach and requested vectors to a downwind to analyze the situation better. After overflying the field we turned cross and downwind to run the checklists and comply with SOP's. We misunderstood a vector and thought as an emergency aircraft we were cleared for the approach. As we were VMC we got within 3 miles of another aircraft while correcting with no loss of separation. We then landed uneventfully; terminated the emergency after clearing the runway and taxied to parking. The aircraft was written up and we briefed the waiting maintenance and FAA personnel. The cause was probably the flap indicator and the cold soaked flap system lag. In this; my first experience with an emergency; I found that a four man crew delayed the analyzing of the problem. It is not something we train for and the division of labor needed to be better defined. This was compounded by the end of a 12:35 flight that was launched out six hours later than scheduled.