How can incitement of imminent lawless action not be constitutionally protected?
The short answer to your question is "because the Supreme Court of the United States said so."
In Brandenburg v. Ohio SCOTUS found that the Constitution protects speech that calls for lawless action in the abstract but does not protect speech "directed to inciting or producing imminent lawless action and is likely to incite or produce such action".
The court's per curiam opinion seems to treat the decision as self-evident - it's quite short after discussing the facts of the case.
However, Justice William O. Douglas wrote a concurring opinion (his "caveat") that discussed and was critical of previous decisions in such cases, including the use of the 'clear and present danger test', so his opinion is useful for a brief history of First Amendment judgments to that point (Brandenburg).
The Declaration of Independence is not law. Following "a history of repeated injuries and usurpations" and failures to reach political settlements it asserts a moral right to overthrow the tyranny of the British crown. It alludes to rights, it does not "enshrine" or create a legal right that the judiciary can interpret. Judges might refer to the Declaration in their judgments, not using it as legal authority but an articulation of fundamental values.