To expand on @user6726's answer, and get into the legal specificities, since the only duty not to do this, really, arises generally out of those predominantly criminal statutes, a "legal action" would resort to a tort action which is "in essence is the breach of a nonconsensual duty owed another. Violation of a statutory duty to another may therefore be a tort and violation of a statute embodying a public policy is generally actionable even though no specific civil remedy is provided in the statute itself. Any injured member of the public for whose benefit the statute was enacted may bring the action. (See Hudson v. Craft,33 Cal.2d 654, 660 [ 204 P.2d 1, 7 A.L.R.2d 696]; Biakanja v. Irving,49 Cal.2d 647, 651 [ 320 P.2d 16, 65 A.L.R.2d 1358]; Wetherton v. Growers Farm Labor Assn.,275 Cal.App.2d 168, 174 [ 79 Cal.Rptr. 543]; McIvor v. Mercer-Fraser Co.,76 Cal.App.2d 247, 253-254 [ 172 P.2d 758].) (Laczko v. Jules Meyers, Inc. (1969) 276 Cal.App.2d 293, 295)
Although these formulations are from California, these basic principles arising out of common law should not substantially differ, say, in Texas where the man resides right now, but surely, some of his flights for Tesla must include California rather frequently any ways.
Additionally, the points @user6726 makes about the frequency, quality, seriousness etc. of any explicit or the mere implied threat is factored in for example in the case of a cause of action for negligent or intentional infliction of emotional distress where "[w]hen there is a breach of duty, "a person who is in the path of negligent conduct and reasonably fears for his or her own safety may recover for resulting emotional distress." In re Air Crash Disaster Near Cerritos, Cal., 973 F.2d 1490, 1493 (9th Cir. 1992). ” [Citation.] (discussing hypothetical pedestrian narrowly avoiding speeding car and indicating that threat of injury is the relevant issue); [Citation.] (quoting Potter hypothetical and holding plaintiff was not precluded from relief simply because car did not actually hit her) (Taylor v. Honeywell Int'l, Inc. (9th Cir. 2015) 599 F. App'x 664, 3)
Analogously, even if he could not show any evidence of threats in innuendo or such made overtly, it is possible that establishing that in his position any reasonable person would fear for their lives, he could be treated as one who was not threatened, but "almost got hit by the threat" given his personal circumstance which inflicted such emotional distress that merits action.
Now, whether or not a criminal violation could be established that is different question, for e.g., whether or not, for purposes of the tort action, him being plaintiff would be required to prove his case merely by the preponderance of the evidence, or the same threshold would be required as if the civil defendant would be under criminal prosecution which could be a question of its own here.
Although true that his flight information is public, it can reasonably be argued that a certain level of expertise knowledge is required for a layman to be able to use the raw, publicly available information to make a threat on his life which would certainly help filter out some wackos even if equally certainly could not prevent any more sophisticated or orginazied attempts on his life.
To decide which one is of greater concern would definitely be a question to be decided by the trier of fact.
