Did kingdoms in ancient Africa have highly trained warriors like that of Europe and Asia? If so what were they called, how were they trained, and what country were they from?
I can speak for West Africa somewhat. Among the Mande peoples of the Sahel region there is a social class known as Donzos who today serve as hunters, and in earlier times served as professional warriors. Donzos are traditionally organized into "Tons" or fraternal bands. Membership in a Donzo Ton is not strictly hereditary and new members could be initiated into a Ton if they learned to follow the Ton's code of conduct. Most Donzo traditionally come from members of the "Horon" caste, who were essentially the "freeborn" or "nobility" of the Mande peoples though members of other castes do join as well. Tons are thus not as strictly defined by a caste system as many other aspects of Mande society. Each Donzo Ton is lead by an elder known as a Donzokuntigi, though Tons are highly egalitarian will often make decisions collectively at gatherings known as tonsigi.
Though are stories of Donzos as far back as the Mali Empire Donzo Tons played a particularily important role in the formation of new states after the fall of the Songhai Empire in the 16th century. A Donzo Ton in service to the Faama or King of Segou was reorganized into an effective fighting force by Bitòn Coulibaly. Coulibaly went on to found the Bambara Empire. Unlike european knights or japanese Samurai, the Donzo do not traditionally own a great deal of land as individuals; they instead live by hunting and selling game from land not used for farming or pastoralism. Donzos are nonetheless highly respected by their communities in Mande society and are commonly called on for defense and security.
Since the end of the colonial era, Donzo Tons have seen a great deal of revival as a source of order and law enforcement by communities that are not protected by state institutions. Donzos have increasingly been drawn to this line of work as revenue from hunting has declined due to the expansion of farmland, overhunting and drought. Donzos today continue serve in Mali and Cote D'Ivoire as vigilantes and as private security under the hire of local elites.
Sources:
Bassett, Thomas J. "Dangerous Pursuits: Hunter Associations ( Donzo Ton) and National Politics in Côte DIvoire." Africa 73, no. 01 (2003): 1-30. doi:10.3366/afr.2003.73.1.1.
Hellweg, Joseph. "Encompassing the State: Sacrifice and Security in the Hunters' Movement of Côte d'Ivoire." Africa Today, 2004, 3-28. http://www.jstor.org/stable/4187608?seq=1#page_scan_tab_contents.
Lilyan, Kesteloot L'EPOPÉE BAMBARA DE SÉGOU I and II, chez Nathan en 1972. Elle fut reprise par L'Harmattan en 1993 France
You might like /u/khosikulu and /u/faceintheblue writing about Zulu impis and amabuthos in this thread on Zulu military power.
If you're specifically interested in the religious aspects of European knighthood - the archetypal knight being essentially a fighting monk, what Le Morte D'Arthur refers to as "apostles" or "goodly men to bear arms" - then you might be interested in reading Yoruba sacred traditions about the Warriors (Guerreros), who show up in American, Caribbean, and Latin American ADTs.
I think /u/firedrops could comment more about that (check out this discussion); reading Joseph Murphy's Santeria: African Spirits in America would probably also be of interest.