The superlative constructions like the king of kings goes back to Old English and it is a borrowing from Biblical Latin (rex regum, saecula saeculorum). It can be ultimately traced back to Hebrew. The book Old English Literature and the Old Testament (edited by Michael Fox, Manish Sharma) mentions that it is a standard way of constructing superlatives in Hebrew and uses the term superlative genitive (or augmentative genitive):
The focus of this article is one specific type of Hebrew syntax adopted in Old English, the so-called augmentative or superlative genitive. In particular, I argue that Cynewulf seems to be aware of the biblical and Hebraic origin of this construction and uses it in his poem Elene to distinguish the diction of the Jewish characters from that of the Christian ones.
In the superlative genitive construction, a noun in any case is modified by the same noun in the genitive plural, raising the meaning of the first noun to the superlative; well-known examples include king of kings, lord of lords, and Song of Songs. Although this construction is used as a means of 'superlation' in pre-Christian Latin, its popularity and wide use in the Christian west is due to its use within the Hebrew Bible and the subsequent translation of the construction into Latin in the Vulgate. The few modern grammars of medieval or ecclesiastical Latin that treat this construction generally attribute its origin to an imitation of the Hebrew.
Seow succinctly defines the Hebrew construction in reference to the opening of Ecclesiastes thus:
The juxtaposition of the singular and the plural of the same noun is the standard way in Hebrew to express the superlative: e.g., ‘king of kings' = 'supreme king' (Dan. 2:37; Ezra 7:12), 'servant of servants' = ‘abject servant (Gen. 9:25), and 'god of gods' = 'highest god' (Deut. 10:17). Thus, hăbēl hăbālim refers to absolute or the ultimate hebel, a word that has been translated as 'vanity."
Absolute superlative is another grammar term used in some sources like the book A Biblical Hebrew Reference Grammar: Second Edition (by Christo H. van der Merwe, Jacobus A. Naud):
30.4.2. Superlative degree
(1) The absolute superlative, which manifests the outstanding feature,
condition or state of something or someone can be expressed by:
(a) A singular noun in the status constructus preceding the indefinite plural form of the same word.
הֲבֵל הֲבָלִים utmost vanities [lit. vanity of vanities] (Eccl. 1:2)*