Before abolition, there were ex-slaves who did work to try and spread their stories and talk about the horrors of slavery through public speaking engagements, yes. Often, they would also have published a book or pamphlet that we call a slave narrative; essentially, an autobiography (Solomon Northup's famous Twelve Years a Slave is an example of one such narrative). One of the most remarkably successful public speakers of the anti-slavery cause in Britain was a man called Olaudah Equiano, who published his narrative in 1789; it was a literary sensation in Britain, printed several times over, and he used the funds from publication and from benefactors to speak all over the country against the slave trade (and to sell more copies!). Equiano's book and subsequent lecture tour is often attributed as one of the factors that helped lead to the abolition of the slave trade by Britain in 1807. Frederick Douglass is perhaps the most famous example from the United States; his remarkable oratory skills and compelling narrative helped elevate him to prominence in abolitionist movement, and he gave many lectures and speeches on the evils of slavery. In many parts of the United States, you could attend meetings of the American Anti-Slavery Society or events put on by them, not unlike you might attend town hall meetings organised by pressure groups today; these helped to create a kind of anti-slavery lecture circuit at which former slaves would often speak.

There are also many contemporary narratives that were written during the struggle for abolition separate from these lecture circuits; literally hundreds and hundreds of them survive to this day. Though their success varied wildly, they were a popular way of highlighting the evils of slavery in white minds. They are, however, fundamentally campaign tools: they were written for a white audience, with the intention of highlighting the evils of slavery, and their 'authors' were usually illiterate slaves working with a white intermediary (who may or may not be open about having written the text). Some are thought now to be outright fabrications by white authors. Whilst they had an educational component they were also campaign tools, and have to be viewed in that way. They do not necessarily reflect what an ex-slave may have put down on paper if they were writing for their own children and grandchildren, for instance, or for future leaders of African American communities.

These are by and large phenomena that occur during the struggle to abolish slavery. After emancipation, interest in the United States tails off because the slavery question is essentially resolved and moves to reconstruction, and the anti-slavery movement is largely wound up at the grass roots level by 1870. The Liberator for example, which was a small but prominent anti-slavery newspaper, ended its 35 year print run in 1865; even though its closing editorial acknowledged there was still a lot of work to be done in ensuring the well-being of ex-slaves, in the mind of its creator William Garrison, it was no longer useful with the abolition of slavery. In that sense then, this is quite a different phenomenon. Holocaust survivors speak in schools to bring history to live to students, to engage them with the subject matter, and to educate us on the lived experience of a tragedy. Whilst contemporary anti-slavery lectures and narratives very much have that function, they were fundamentally part of an ongoing political and social struggle in society. Though a flawed comparison, seeing an ex-slave speak before the Civil War is perhaps more akin to hearing the testimony of an escaped dissident from a country like North Korea than going to hear a Holocaust survivor recount their personal story.

As others have noted in the thread, we also have the WPA Narratives, which are perhaps a little more like your Holocaust example. They are interviews with ex-slaves carried out during the 1930s as a means of providing paid work to unemployed writers during the economic hardship of the Great Depression and encompass hundreds of interviews - some still being discovered! - with former slaves. Some are longer, some are shorter, and their testimony is rich and varied. Now, this is a rather different project in the sense that these interviews are not really intended for mass consumption or for general education in the way a Holocaust survivor touring local schools are - they are really just a way of giving unemployed writers work, on a project they're not necessarily enthusiastic about and which has no grand over-arching objectives beyond that and documenting experiences. They aren't really a 'study' or an education tool in and of themselves - they're just a collection of interviews.

Now, there's been a bit of a discussion in this thread about their usefulness and validity. This is something that historians have fiercely debated over the years; for a time, the orthodoxy was that all slave narratives were useless to us - that view is now discredited, but there are some historians who still instinctively shy away from using them. This stems from the observations that /u/swuboo has rightly made: these are interviews carried out by people who had usually never met these ex-slaves, who were usually reasonably educated white men, and who were chosen because they needed work without much scrutiny of their personal or professional qualifications. They aren't anthropologists or sociologists who have some idea of how to conduct an interview with minimal impact. Perhaps most problematically, we have no idea in almost all cases what questions were asked - meaning we cannot detect explicitly the influence interviewers had on their subjects. There is, for example, new evidence forthcoming soon that ex-slaves are significantly less likely to allude to sexual abuse when asked questions by a white interviewer than a black interviewer. The interviewers in these cases, especially the white interviewers, occupy a position of privilege and power both within wider society and within the specific social dynamics of the interview. As a result, just as the written narratives are distorted by privileged intervention, so too are the interview transcripts.

In 1988, Gayatri Spivak published an article called "Can the Subaltern Speak?"; though her phrasing of her conclusion has been a source of much confusion and anger, her argument was essentially that it is never possible to hear the voice of oppressed people in the historical record authentically. Our records of the oppressed always come to us through the framework of the power structures that oppress them; there is always something of the oppressor that distorts the representation of the experience of the oppressed. There's been a lot of debate surrounding how true that is but certainly in this case, Spivak's idea is essentially correct. Ex-slave experience in the historical record is distorted by the fact it can only reach us through white (and rarely, privileged black) intermediaries, who - even if they are well-meaning - will shape and distort it. When historians use these sources then, they have to be exceptionally critical and careful in their analysis. I wrote a little about this for a Monday Methods thread a while ago here, talking about the use of written narratives. They are still useful - there is still an authentic experience there to identify - but we must be very careful to not take anything at face value, and no one particular source is useful on its own; you have to look for the broader patterns and themes, and for the things that stand out from those patterns.

There are two great digital resources for these documents. The first is the North American Slave Narratives collection digitised by the University of North Carolina, which is a comprehensive collection of written narratives presented in HTML format. The other is the Library of Congress WPA Narrative collection. If you have access to it, you can also get The Liberator's complete archive online via some databases, which often contains articles by African American authors or talks about the lectures and talks people like Douglass were giving in the mid 19th Century.