Nixon made similar assertions of unlimited executive privilege. Even after he resigned he continued to assert that "When the President does it, that means it's not illegal". My understanding is that these claims were rejected by the courts (eg he was forced hand over the critical tapes). The Court also ruled against Bill Clinton's attempt to invoke executive privilege in the Paula Jones case.
https://edition.cnn.com/2018/05/02/p...ege/index.html
I'm no constitutional law expert, but I assume that the Supreme Court would again reject such extreme assertions if it came to the test, which it probably will at some point. The scary question is what happens if Trump simply defies their decisions.