The pairing with Parashah Korach, whose central episode is Korach's open rebellion against Moses and Aaron's leadership, accusing them of exalting themselves improperly over the rest of the community, rests on Samuel's own public defense of his integrity as leader, a direct answer to the same kind of accusation Korach had leveled generations earlier, even though no one in the haftarah has actually accused Samuel of anything at the moment he speaks.
Samuel's public question, whether he has ever taken so much as an ox or a donkey or accepted a bribe, mirrors precisely the standard Moses himself invokes when responding to Korach's rebellion, that he has never taken so much as a single donkey from anyone he has led, a nearly identical form of self defense used by two different leaders confronting, in one case directly and in the other only implicitly, a challenge to their own legitimacy.
The haftarah's treatment of the people's demand for a king as itself a kind of rejection of God's direct rule also echoes the deeper question Korach's rebellion raises about where legitimate authority actually comes from, both texts affirming that authority properly recognized by God cannot be seized by popular demand or by force, whether that demand takes the form of Korach's open challenge or the nation's own request for a king to rule over them instead.