Part of the issue in answering this question is nomenclature, and what is implied by this statement. There was no Islamic conquest of "Africa." The conquests in the early years after the death of Muhammed were all centered on North Africa and made very little, if any advancement south of the Sahara. The spread of Islam south of the Sahara is a very broad and varied topic which we cannot get into detail here because of its varied and localized nature.

Now onto the issue of slavery in North Africa and Middle East from the 7th century until the 20th century. This is again a very broad and varied topic to which is it difficult to say too many specifics. A slave in 7th century Mecca would find themselves in a very different situation than a palace slave in 19th century Istanbul, or a domestic slave in 13th century Cairo. It is important to remember that Subsaharan Africa was just one source of slaves. Slaves came from a multitude of localities and not just Subsahran Africa. It is also important to remember that many groups south of the Sahara had their own local systems and slave trade. These trades sometimes fed into the broader slave trade. The main regions Subsaharan slaves originated from were Bilad as-Sudan (The Sahel region), Nubia, Ethiopia, and East Africa. During different times these regions played varying degrees of importance in the slave trade. In some cases these trade networks built upon local trade networks (for example in West Africa and Ethiopia), in the case of Nubia slaves were sent to Egypt as part of annual tribute, and in the case of East Africa, slaves were forcibly captured by slave traders. The number of slaves taken from Subsaharan Africa is difficult to enumerate, it's a very long period of history and records often don't exist or are incomplete. Estimates are generally given to be around 10,000,000, which is about the same as the estimate for the Trans-Atlantic slave trade. The number however, is far from being settled and we cannot speak with certainty how many were involved.

As for the part about it officially ending in about 1969, this is isn't exactly correct. It seems to be alluding to approximately the time most Gulf countries formally abolished slavery. The statement however says, "Muslim slavery." The Gulf is just one part of the larger Muslim world, and at the time a relatively small portion of the Muslim world population wise. It also insinuates some disconnect between Muslim and "African." These are not exclusive categories.

Finally, it is important to remember what is sometimes implied in these kinds of statements (which seem to be popping up on Reddit and other places somewhat frequently). There seems to be a constant comparison between the Trans-Atlantic slave trade and Trans-Saharan/Indian Ocean slave trade, especially as to which one was "worse." This is a mistake. While we can of course compare and contrast both systems, it is important to understand them within their own contexts and realize it's not a contest to see who was "worse," especially if it is used as a means to shift attention away from the harsh realities of the Trans-Atlantic slave trade.

There is also the issue of who exactly are we talking about? Are we talking about Islam? Are we talking about Muslims? Are we talking about Arabs? Are we talking about Africans? Are we talking about Black people? These categories are not as clear cut as these types of simple statements make them. North Africa, the Middle East and Subsaharan Africa during the long time period were multi-religious and multi-ethnic societies. There are many places where the categories become blurred. Take the infamous slave trader Tippu Tip as an example. He was simultaneously Arab, African, and Black. Someone whose preferred language was not Arabic, but an African language. The Trans-Saharan/Indian Ocean slave trade came out of a particular historical context and development that blurred racial and ethnic categorizations. Bringing racial and ethnic foreign ethnic and racial categories will quickly skew the understanding of how it operated. The Trans-Saharan/Indian Ocean slave trade is is a significant and important part of history to study and learn about, but it is important to do so within its own historical context and understanding.

If you're interested in a further discussion on this please read "Slavery, Genocide and the Politics of Outrage" by Hishaam D. Aidi.

A few more things to consider in addition to u/tropical_chancer 's excellent response.

First, that the interval in which sub-Saharan African populations were taken into slavery in North Africa, Egypt, the Arabian Peninsula, the Levant and Mesopotamia, and other parts of the Mediterranean and Middle East, stretches back to pre-Islamic history. The spread of Islam changed the density and culture of trans-Saharan and East African trading routes but it did not create those networks from nothing. So that even if the sum totals of sub-Saharan individuals transported as captives across those networks approaches as many as ten million people, it's over an interval of approximately 1,500 years from a very large and diffuse area of the continent. The Atlantic slave trade, in contrast, took 15-20 million people in an interval of roughly 350 years, with the bulk of that happening in a single century, and largely from a smaller total area. That is a huge difference in terms of consequentially destructive impacts on the African societies affected.

Second, the specificity of the knowledge we have about the two slave trades is dramatically different and that will remain true in the future. Estimates of the numbers involved in the Atlantic slave trade are now based on painstaking archival research drawing on ship manifests, port records, taxation records, journals, eyewitness accounts, etc. We have nothing like that for the trans-Saharan and East African coastal trades--it's almost entirely a matter of inference and estimates from a very thin documentary record.

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Third, for the most part, Africans taken into slavery via these routes were not chattel slaves of the sort the characterized the "plantation complex" in the Americas during the Atlantic slave trade. They were often subject to the same kinds of enslavement that were present in some sub-Saharan African societies, involving domestic service, military conscription, or administrative work in courts or centers of power, and were often manumitted during their own lives, or their children were manumitted. There were areas of the Middle East where slave labor largely from sub-Saharan Africa was employed on a larger scale--we know this partly from a famous slave revolt during the Abbasid Caliphate, called the Zanj Rebellion. The historian Ghada Hashem Talhami argued in 1977 essay that this revolt wasn't exclusively of slaves of African descent but instead involved a whole range of people who were marginalized or oppressed by Abbasid rule, but even Talhami acknowledges that field slaves of African descent were involved in some fashion.

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Paul Lovejoy's Transformations in Slavery is a good place to start to try and get some sense of the relationship between the "Islamic slave trade" and the Atlantic slave trade, but it's really important to not accept simple or false equivalencies in that comparison.

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