The first widely published English Bible was the Tyndale bible, which heavily influenced the Geneva Bible, both of which is what the KJV is mostly based on and competed with until King James banned the Geneva Bible.

While no Bible mentions or supports capitalism for the reasons you mentioned, both of those earlier translations had an anti-authoritarian bent to them that King James certainly didn't like, and had edited.

Soon after Elizabeth I took the throne in 1558, the flaws of both the Great Bible and the Geneva Bible (namely, that the Geneva Bible did not "conform to the ecclesiology and reflect the episcopal structure of the Church of England and its beliefs about an ordained clergy") became painfully apparent.

The Bishop of London added a qualification that the translators would add no marginal notes (which had been an issue in the Geneva Bible). King James cited two passages in the Geneva translation where he found the marginal notes offensive to the principles of divinely ordained royal supremacy: Exodus 1:19, where the Geneva Bible notes had commended the example of civil disobedience to the Egyptian Pharaoh showed by the Hebrew midwives, and also II Chronicles 15:16, where the Geneva Bible had criticized King Asa for not having executed his idolatrous 'mother', Queen Maachah (Maachah had actually been Asa's grandmother, but James considered the Geneva Bible reference as sanctioning the execution of his own mother Mary, Queen of Scots). Further, the King gave the translators instructions designed to guarantee that the new version would conform to the ecclesiology of the Church of England. Certain Greek and Hebrew words were to be translated in a manner that reflected the traditional usage of the church. For example, old ecclesiastical words such as the word "church" were to be retained and not to be translated as "congregation". The new translation would reflect the episcopal structure of the Church of England and traditional beliefs about ordained clergy.

Tyndale's use of the word 'Congregation' instead of church had pretty far reaching implications:

When Tyndale translated the Greek word ἐκκλησία (ekklēsía) as congregation, he was thereby undermining the entire structure of the Catholic Church.

Many of the reform movements believed in the authority of scripture alone. To them it dictated how a "true" church should be organized and administered. By changing the translation from church to congregation Tyndale was providing ammunition for the beliefs of the reformers. Their belief that the church was not a visible systematized institution but a body defined by believers, however organized, who held a specifically Protestant understanding of the Gospel and salvation was now to be found directly in Tyndale's translation of Scripture.

I wouldn't say any of that explains how the KJV would influence religious conservatives to support capitalism, but I guess it could potentially have an influence over an acceptance of dogmatism within the Republican party? But I think most religious people don't actually read the Bible anyway, so even that is a stretch. The more likely explanation is due to Protestant 'work ethic' as mentioned by @Copernican@lemmy.world