in 1935 Hitler passed a law that said that only two flags could be flown in Germany: the swastika and the Zionist banner. This is not something I'm 'claiming;' this is not just one book.
A similarly worded claim reported in the Guardian to be by Livingstone:
Speaking to the Guardian on Friday, Livingstone praised Lenni Brenner, the author of Zionism in the Age of the Dictators, and said the book was full of details that he would cite in his defence.
“All the detail is in there. The striking thing that does confirm there was an ongoing dialogue between the Zionists and Nazi government is, in 1935 Hitler passed a law banning any flag being displayed except the swastika and the blue and white Zionist flag, which is pretty amazing.”
He added of Brenner’s book: “It confirms there was clearly an ongoing dialogue, even if the Israeli government now tries to pretend that none of that all happened.”
The Wikipedia article Flag of Israel has a section on it being referenced in the Nuremberg Laws, which were passed in 1935.
Paragraph 4 in "The Laws for the Protection of German Blood and German Honour", part of the infamous Nazi Nuremberg Laws of 1935, states that 1. "Jews are forbidden to display the Reich and national flag or the [German] national colours. 2. On the other hand, they are permitted to display the Jewish colours. The exercise of this right is protected by the State." Paragraph 5.3 described the penalty for infringing "1": up to one year's imprisonment plus fine, or one of these. The "Jewish colours" referred to in this article were blue and white.
Wikipedia's article on the Nuremberg laws also concurs.
However, while that law does make mention of Jews being forbidden from flying German flags, and Jews being legally allowed (at least in theory) to fly "Jewish colours", it doesn't make any mention of Jews being banned from flying the flags of other countries, or flags that aren't associated with countries (such as the pride flag, except it didn't exist at that time), nor does it say what flags non-Jews can or cannot fly.
Related question: Did Hitler support zionism?