According to Chapter 15 of A People's History of the United States, why was communism so prevalent during and after the 1920's?
Is the reason why because the common man lost faith in the old style of politics, where there was only two parties, the Republicans and Democrats, and as result of both parties favoring the haves(the elite and big business), the common man saw another style of government the communist party.
I would say that the reason you give here is related to the main reason for the popularity of communism, but is not actually the main reason. The main reason for the prevalence of communism during this time was the fact that the economic system of the United States was (to Zinn) oppressive and exploitative. In other words, the economic system favored the haves so much and was so brutal to the have nots that many of them turned to communism. Of course, if the two major parties had enacted more pro-poor or pro-worker legislation people might not have become communists, but the main cause of their discontent was economic, not political.
The most important part of the chapter with regard to this question is the part where Zinn describes the so-called prosperity of the 1920s. There, he says that the prosperity was only for a very few people. He cites the famous "Middletown" study that showed how harsh life was for workers in Muncie, IN. He talks about how many people were killed or injured on the job each year in the country as a whole. The point he is making is that the prosperity of the '20s was only for a few and that the masses were exploited and oppressed. This, to Zinn, is why communism was so prevalent.