You are attempting to compare three pieces that were written under very different circumstances from each other over a range of time when conditions changed greatly. Finding similarities between the pieces is much more difficult than identifying differences.
The Declaration of Independence was written as an announcement and explanation of the course of action being taken by the colonies in separating themselves from Great Britain. The language is formal and structured to present evidence that would justify the revolutionary process to the rest of the world.
We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain inalienable Rights, that among these are Life, Liberty and the pursuit of Happiness...whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government.
The Gettysburg Address was written to pay tribute to fallen soldiers and to dedicate the cemetary in which they were buried. There is some similarity with the Declaration of Independence in the call to those listening to the Gettysburg Address to come together and bring the Civil War to an end.
It is for us the living, rather, to be dedicated here to the unfinished work which they who fought here have thus far so nobly advanced. It is rather for us to be here dedicated to the great task remaining before us
The "I Have a Dream" speech is also a call to action. After presenting examples of the hardships and injustices that had been inflicted upon the Negro people for hundreds of years (similar to the reasons for revolt presented in the Declaration of Independence), the speech encourages listeners to press on with efforts to bring about a resolution to the struggles being faced (similar to the Gettysburg Address's purpose).
the Negro is still sadly crippled by the manacles of segregation and the chains of discrimination...the Negro lives on a lonely island of poverty in the midst of a vast ocean of material prosperity...the Negro is still languishing in the corners of American society and finds himself an exile in his own land.
This speech alludes to the Gettysburg Address by copying the format of its opening statement.
All three pieces were written at turning points in the history of the United States. All three express deep awareness of the events that made necessary the writing of the documents, and all three present articulate and detailed justifications for the calls for action that were sounded.