While I agree with pohnpel397 that, in his speech, Martin Luther King Jr refers in general to injustices, a listener can draw some specific situations from his references.
When he refers to the Emancipation Declaration of 100 previous to his speech, and the continuing suffering of the African American in the "manacles of segregation", he is referring to each of the individual laws in counties and states around the nation that keep African Americans segregated from equitable access to wealth and resources. This he sees as injustice on a national scale.
The very fact that this speech was delivered at a March on Washington for Jobs and Freedom reinforces the idea that there was a systemic miscarriage of justice against African American citizens.
When King mentions police brutality, he is referring to all incidents of violence by law enforcement against African Americans and against people working for civil rights. The most famous of these was on 3 May 1963, just months before King's speech, when police used firehoses and attack dogs to repel a non-violent crowd of African American adults and children in Birmingham.
There is no doubt that those listening to King's speech were able to conjure up images of these individual cases of injustice, when he spoke in general terms. In fact, due to the alarming number of cases of injustice, the use of generalisations allowed King to communicate with the widest possible audience about his cause.
In this speech, King does not cite any specific acts of injustice towards any individual African Americans. Instead, he speaks in general terms about the sorts of injustices suffered by all African Americans. King talks about police brutality. He talks about segregation in motels and hotels. He talks about residential segregation and "white only" signs on drinking fountains. He talks about the denial of the right to vote. This is as specific as King gets in this speech. He is talking about general kinds of injustice, not about specific incidents of injustice to individuals.