If one accepts Noonan was flying under and overcast, previously it was my assumption Noonan was operating pure DR with wind speed and direction unknown. Based on a article I found this is not necessarily true. In a March 22, 1936 article printed in the Baltimore Sun Noonan made much of PanAm's ability to determine drift angle, and I presume, wind speed and direction, by dropping either flairs or aluminium powder bombs. Either created a fixed point on the ocean surface from which drift could be measured. The Luke Field Inventory has item 30 12 Aircraft Water Lights and item 31 7 Aluminium Direction Bombs. So, it appears at the time of the Luke Field accident Noonan had equipment on board allowing him to measure drift angle and by wind triangle wind speed and direction. I think any assumption he did not have and did not use this capability on the Lae Howland flight would be a dangerous one.
It is my surmise: Being careful to maintain a fixed speed and altitude throughout drop the flair. Go thru a procedure turn as you would to return to a non-directional beacon. Line up the flair on the reciprocal course and crank in wind correction to make the flair stand still left to right in the windshield. Pass the flair. Another procedure turn and line up the flair on your original course. Again crank in wind correction until it stands still and fly on with the wind correction made. Your navigator should in addition be able to draw two wind triangles that show the wind coming from the same speed and direction.