Answer:
The quote "Westward fled the refugees from this new Sahara, as if obedient to the old American tradition that westward lies the land of promise." simply means:
Since Oklahoma was experiencing sand storms, it became a "new Sahara" and people deserted the area, became refugees seeking for a better place (like a promise land) and they went westward (California) as if they were obeying the Old American tradition that says westward lies the land of promise. So they thought going westward will be far better.
Step-by-step explanation:
During the period of the sand storms in Oklahoma around 1934 and 1935, there was a great influx of people into California and other western coasts which was considered as a promise land. At this time, there was competition for jobs among the dwellers of the land. People were in desperate need of a means of livelihood. Some of them kept moving even till northward during the harvests.
The quote was culled from "Since Yesterday: The 1930s in America," written by Frederick Lewis Allen.