Śrīla Viśvanātha Cakravartī Ṭhākura has commented extensively on this verse. To explain the word maṇibhiḥ — “(Kāliya worshiped the Lord) with jewels” — the ācārya has quoted from the Śrī Rādhā-kṛṣṇa-gaṇoddeśa-dīpikā, by Rūpa Gosvāmī, as follows:

kaustubhākhyo maṇir yena
 praviśya hradam auragam
kāliya-preyasi-vṛnda-
 hastair ātmopahāritaḥ

“The Lord had made His Kaustubha gem enter the serpent’s lake, and then He arranged for it to be presented to Himself by the hands of Kāliya’s wives.” In other words, because Lord Kṛṣṇa wanted to act just like an ordinary human being, He made the transcendental Kaustubha gem invisible and caused it to enter within Kāliya’s treasury. Then when the appropriate moment came for Kāliya to worship the Lord with many different jewels and ornaments, the serpent’s wives, unaware of the Lord’s transcendental trick, presented Him with the Kaustubha gem, thinking it was simply one of the jewels in their possession.

The ācārya has further commented that the reason Lord Kṛṣṇa is described in this verse as garuḍa-dhvaja, “He whose flag is marked by the symbol of His carrier, Garuḍa,” is that Kāliya also desired to become Lord Kṛṣṇa’s carrier. Garuḍa and the serpents are originally related as brothers, and therefore Kāliya wanted to indicate to Lord Kṛṣṇa, “If You ever have to go to a distant place, You should also think of me as Your personal carrier. I am the servant of Your servant, and in the wink of an eye I can travel hundreds of millions of yojanas.” Thus the Purāṇas narrate that in the course of Lord Kṛṣṇa’s eternal cycle of pastimes, when Kaṁsa orders the Lord to come to Mathurā, He sometimes goes there mounted upon Kāliya.

Thus end the purports of the humble servants of His Divine Grace A.C. Bhaktivedanta Swami Prabhupāda to the Tenth Canto, Sixteenth Chapter, of the Śrīmad-Bhāgavatam, entitled “Kṛṣṇa Chastises the Serpent Kāliya.”