What are some examples from Dr. King's speech that showed the ideas of the Declaration of Independence were not being met for African-Americans?can...

I am assuming that you are asking about the "I Have A
Dream" speech and that you are referring to the part of the Declaration of Independence
that talks about all "men" being created equal.  I have edited your question
accordingly.

In this speech, Dr. King talks mostly in
generalities about the way he thinks America ought to be.  However, he does, at times,
give specific examples of ways in which he thinks that America has failed to treat all
people equally.

King talks about the injustice of
segregation.  He talks about travelers being unable to find lodging in segregated
hotels.  He talks about children being scarred by the "whites only" signs.  He talks
about the injustice of segregated housing.  He also talks about how unjust it is that
blacks have so many obstacles between them and the ability to vote.  Here is the most
salient passage from the speech:

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We can never be satisfied as long as our bodies,
heavy with the fatigue of travel, cannot gain lodging in the motels of the highways and
the hotels of the cities. We cannot be satisfied as long as the negro's basic mobility
is from a smaller ghetto to a larger one. We can never be satisfied as long as our
children are stripped of their self-hood and robbed of their dignity by signs stating:
"For Whites Only." We cannot be satisfied as long as a Negro in Mississippi cannot
vote...