First, you have to know that the flag before was ruled in the "Verfassung des deutschen Reiche"( that's the constitution of the Weimarer Republik) in article 3: "Die Reichsfarben sind schwarz-rot-gold." ("The colors of the Reich are black-red-gold.") This wasn't popular with the more right-leaning elements to begin with. The more conservative and reactionaries and also the nationalists (including the NSDAP later) actually hated the new flag. The black-red-gold was a symbol of the (Vormärz and the Studentenbünde, which lead to the) 1848 uprisings, that, while nationalistic, were fairly liberal and had a tradition of being claimed by the rather left in the Weimarer Republik. (There were also rightwingers, which supported the black-red-gold flag, but they were silenced by 1935 in that matter). In short, the old, red-white-black flag became the symbol of nostalgia and antidemocratic aspects of the right during the Weimarer Republik. Consequently, when Hindenburg (who, as we might recall, was a Prussian officer and later a old-Reich general and a devotee of royal Prussia) was Reichspräsident, he issued a decree in March 1933, that the old Imperial flag was to be used alongside with the Nazi flag on public buildings (as the text states it "until the flag-question is solved").

After Hindenburg died in August 1934, the Nazis made the swastika-flag the sole flag in September 1935 as OP stated.

This was as a passed alongside of the Nürnberger Gesetze, of which, frankly, this should be the easier part to communicate to anyone. However, the populace (the not Jewish part at least) seemed to be strangely unaffected or even in favor of the Nürnberger Gesetze in general.

One thing that lead to discontent, however, was the prohibition of any other flag, meaning that (catholic) churches couldn't raise the papal flag on religious holidays, which they had done before. Some priests got into problems with the local Nazis because of that.