I've been searching, without success so far on mainstream history media (mainly references given by teachers, references on Wikipedia and stuff like this) and have not found any evidences (or proofs of the contrary) about trades between the various African Kingdoms/Empires during the Mamluk's Sultanate ruling in Egypt - half of the 13th century -> first quarter of the 16th century.
As far as I Know, The Ethiopian Empire wasn't very far from the Mamluk' Sultanate, yet I've found no proof of any known trade route. Was it because of religious differences ?
On the other coast, The Malian Empire and The Kanem Empire weren't very far either, no sources about trade routes between the two either…
Does anyone know where to search about this peculiar subject? The only things I found were between the various north-African kingdoms.
This article on Precolonial trade in Africa by the Oxford Research Encyclopedia should give you a number of good starting points. It goes through just about everywhere one might expect trade to occur, complete with references to primary sources, including but not limited to:
Coastal trade on the East and West coasts.
River trade along the Nile, the Zambezi, the Niger, etc.
The Trans-Saharan trade.
See the interesting diary published as 'Travels in the Interior of Africa' by late Eighteenth Century British explorer Mungo Park. He travelled through inland Sub-Saharan West Africa, learned local languages and traced much of the course of the River Niger. The rest of this answer is based on that.
Park records that trade among the Africans of that region was sufficiently extensive at that date that there was a class of professional merchants called 'Slatees'. They were prosperous enough to have their own retinues of assistants and numerous enough that several bound for the same destination would travel together in 'caravans' or 'convoys' for mutual defence against robbers and wild animals. They traded in various articles e.g. salt, cloth, iron, honey, locally brewed mead and by that date imported European manufactured goods including muskets, gunpowder and ammunition and imported spirits, especially rum, usually sold 50% diluted with water.
However, above all, sadly, the slatees dealt in slaves.
The society was largely illiterate so the slatees left few if any written financial accounts, contracts or other records. That may have limited the scale to which it was practical for their enterprises to grow.
Trade was basically barter although in some areas imported cowrie shells were used as currency. In others 'bars' became almost a notional currency; custom fixed the quantities of other goods equivalent in value to an iron bar, so one could e.g. trade a 'bar' of salt for a 'bar' of amber without any actual bar being involved.
Park also recounts the value of a 'prime' slave being used in a similar way; at one point he collects a debt from a native African merchant to a European one living some distance away in the form of 'goods to the value of 5 prime slaves'.
Long-distance trade routes could cross through several African kingdoms although the ruler of each would expect, demand or just seize a share of goods people carried through his kingdom. Some kings had the reputation of being greedier about this than others.
Some goods were mostly traded for consumption within Africa. Salt traded from the coast was sufficiently expensive in areas far inland that 'he eats salt with his food' was a customary way of saying 'he is a rich man'.
Other goods like ivory were mostly traded because they could be sold to Europeans on the coast. Africans could not understand why Europeans wanted it. Even if shown European knives made with ivory handles, Africans did not understand why Europeans used ivory when wood would serve the same purpose and was less difficult and dangerous to obtain [Elephants are more likely to fight back than trees!]
Slaves were a particular item of long-distance trade in part because prisoners taken in wars between neighbouring African kingdoms, if kept in the locality, might try to escape to get home. Consequently, the value of a captured slave increased the further away they were from their original home, because the harder it would be for them to find their way home the less likely they were to try to escape.
This was one reason why it was commercially attractive to sell slaves to white men who would take the slaves on board ship far across the sea.
Hence by the time Park was writing, the slave trade to the Americas probably increased the value of and hence commerce in slaves and wars and kidnapping within Africa with a view to capturing slaves, although that was by no means the only reason for warfare.
Park believed that slavery was a very ancient institution in Africa. There were different types of slave, some of whom such as the recently captured could be sold out of the locality at will. Others born into slavery, by strong custom, could only be sold away from their homes as a punishment for misconduct or in cases of necessity such as during a famine.