Reddit reviews Tell This in My Memory: Stories of Enslavement from Egypt, Sudan, and the Ottoman Empire
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Used Book in Good Condition
More to the precise point of your question -- for most of the Middle East slavery existed only in memory by 1962. The slave trade had been dismantled for almost a century (the slave trade had been outlawed, if not terribly well enforced, in varying degrees beginning in the mid-19th century) and the last people to hold slaves were those who came from elite Ottoman families wealthy enough to own household slaves (concubines, which were typically Circassian, and eunuchs, typically Sub-Saharan). As the discussion below between /u/Trigorin and /u/i_like_jam details, Ottoman/Islamic slavery was a different animal when compared to the European variety -- but most importantly to the discussion of Malcom X (and other civil rights leaders) is that in the Middle East, slavery created very different associations and feelings about race. Not to say that race and slavery were not tied in the Middle East, but those bonds were definitely different (and had different aftereffects) than in the US or Europe. For instance, a "black" person descendant from Islamic slavery often doesn't have the same sort of associations as a "black" person in the US, nor do they really feel that they've lived though similar conditions. In fact, the lives of "black" people in the Middle East after the end of slavery has arguably been a more sordid one than in the US (thanks in large part of colonization and de-colonization, economic hardship and civil war), and this is not lost on many sub-saharan Africans living in places like Egypt.
So directly to your question, how aware was Malcom X of these phenomena prior to making Haj? I doubt he knew much, and he certainly wasn't exposed to much while he was there. It should be understood that Malcom X didn't make Haj the way most of the billion plus Muslims make Haj. He rolled up to Mecca in Bentley. He was being watched by the CIA. He was a celebrity, and he was treated like one, especially by the Saudis.
Some additional reading material:
Eve Troutt Powell A Different Shade of Colonialism and Tell This in My Memory
Ehud Toledano As If Silent and Absent
The edited volume Black Routes to Islam is also essential for the relationship between African Americans and the Islamic world.
Slaves in the Middle East weren't all African. Here are some books that can give you a better perspective on slavery in the Islamic world:
http://www.amazon.com/Race-Slavery-Middle-East-Historical/dp/0195053265/ref=sr_1_1?ie=UTF8&qid=1353987039&sr=8-1&keywords=bernard+lewis+race+and+slavery
http://www.amazon.com/Tell-This-My-Memory-Enslavement/dp/0804782334/ref=sr_1_1?s=books&ie=UTF8&qid=1353987192&sr=1-1&keywords=eve+troutt+powell
http://www.amazon.com/Women-Slavery-Late-Ottoman-Empire/dp/1107411459/ref=sr_1_2?s=books&ie=UTF8&qid=1353987281&sr=1-2&keywords=madeline+zilfi
EDIT: I think it's important to note that I don't have some sort of pro white revisionist history agenda, I just think it's important to know that Europeans were not the only ones who had slaves. I say this as a half Arab myself.