The worst effects of the Dust Bowl were after 1933 (in 1935-1938, to be exact). This might in fact explain Roosevelt decline in the plains states after 1936.
That along with the region from the plains to the midwest having a lot of german americans who swung towards Wilkie and stayed with the GOP. (Although im in the opinion that these german american voters would had swung back to the GOP and Wilkie only accelerated it). Its interesting how despite articles saying millions of people moved from the plains to other regions. In fact electoral participation numbers wise in the plains state actually went up. My guess is that a lot of the people affected didnt care much about elections in general and the population that stayed was really buoyed by Wilkie, along with a lot of the post-dust bowl migration being overstated.