B737-800 First Officer reported a flap malfunction while on initial approach. A second approach was completed successfully with a non-standard flap position. The First Officer had 2 suggestions concerning the QRH procedures for this flap malfunction.

Narrative

I was First Officer and Pilot Flying. The aircraft was on ILS XXR; near 'ZZZZZ'; the final approach fix; when we noticed a split flaps indication. The flaps needles split approximately 2mm; with both needles remained in Flaps 30 white band. I executed a go-around with landing gear up and flaps handle remained at flaps 30 due to my knowledge of the QRH 'Trailing Edge Flap Asymmetry' where it instructs to set the flaps lever to current/smallest flaps position. Once leveled off at 3;000 feet; I commanded landing gear down to silence the gear horn. The Captain informed me that the flaps needles was no longer split. I verified and commanded flaps 15. The flaps did not move. We ran the QRH 'Trailing Edge Flap Disagree'; flaps handle was left at 15. Landing was made with Flaps indicated 30. I did not feel any flaps asymmetry. The aircraft handled exactly like how it should be with Flaps 30. After touching down; as the speedbrake was deploying; I heard what sounded like the T/O config warning horn went off for 1 second. Approach; landing; and rollout were normal. After rollout; we noticed the flaps indicator was showing flaps 15. Post-flight walk around confirmed the flaps were at 15.Because of the intermittent failure (1) it is best leave the flaps at 30 from go-around all the way to the second landing without changing flaps position as they might not extend again. (2) QRH 'Trailing Edge Flap Disagree' does not instruct pilot to move the flaps handle to the current indicated flaps position. The flaps could potentially move from 30 to 15 during approach or landing phase because of the intermittent failure. This could have caused a low-speed event or a tail strike.