Start with the premise that Person A has so far engaged only in speech, which is presumptively protected by the First Amendment. So unless the speech is for some reason unprotected, the police should not involve themselves.
This of course begs the question of whether this speech is protected. The First Amendment does not protect "true threats," which includes "those statements where the speaker means to communicate a serious expression of an intent to commit an act of unlawful violence to a particular individual or group of individuals." Virginia v. Black, 538 U.S. 343 (2003).
So the question for the police is whether Person A's texts were meant to communicate a serious intent to commit an act of unlawful violence. Removing First Amendment protection won't be as simple as letting B testify that he truly felt threatened, as the question is whether A meant to communicate a threat. But that also means that for A, it won't be enough to simply deny any violent intent, so the "nothing illegal" disclaimer won't be enough.
In the end, this is a question for a jury to decide, should the case ever reach that far. The jury would essentially be asked to engage in mind-reading, determining what A was thinking when he sent those texts. The jury should be instructed to take several factors into consideration when it makes that decision, including the "context" of the remarks (the explicit disclaimer of violence helps A), the "conditional nature" of the threat (the three-strikes langauge helps A), and the "reaction of the listener" (calling the police hurts A). Watts v. United States, 394 U.S. 705, 708 (1969).
Practically speaking, if B were to call the police, I'd expect them not to investigate, unless they were awfully bored. If they decided to, I don't think there would be any actionable violation of A's rights, given their obvious inability to divine A's intent based solely on B's account. A court would likely allow them to investigate, but I doubt a prosecutor would allow them to bring charges based on the facts you've described.