I’ve searched through a variety of sources and come up empty. This isn’t mentioned in Righteous Victims by Benny Morris, 1967 by Tom Segev, or Six Days of War by Michael Oren. It’s not found in “The Fall of Jerusalem, 1967” by S. Abdullah Schleifer in Journal of Palestine Studies. It’s not in “On the Use of Air Power and Its Effect on the Outbreak of the Six Day War” by Moshe Gat in The Journal of Military History.

Virtually all of these sources refer to the use of napalm only on military targets.

The only places I’ve seen it mentioned are tracked to Arthur C. Forrest, whose book I do not have and have only seen second-hand reference to. His claims mirror some news reporting in Christian Science Monitor and the New York Times that I’ve seen in other secondhand sources. I’m explaining all this so you can see the rabbit hole I went down to try and answer this. I followed a lot of sources as far as I could.

I couldn’t get the relevant CSMonitor archive, but did find the June 12, 1967 article in the NYT cited. It claims Israel appeared to have bombed refugees fleeing, but doesn’t say napalm was used, nor does the article mention the context or extent of such an event. No source I’ve managed to track down does.

The only claim I’ve yet to investigate and distinguish (napalm versus claims that civilians were strafed, in all cases the allegations mention guns or other ordnance, not napalm) is sourced to a team of doctors who claimed that napalm hit fleeing refugees. The claim is found in various books citing Forrest, who is citing General Glubb, who is citing a statement by a team of doctors from American University of Beirut. There is technically another claim by an American activist writing in Al Anwar, but this claim is uncorroborated and based on a walk through of an Egyptian hospital well after the war ended, which does not seem wholly credible.

Forrest's claims about Glubb's statements are always labeled the same way and in the same outlets quite hostile to Israel, and as noted I can't get ahold of Forrest's book. None of them actually say what Forrest is citing to of Glubb's, and I've done as much research as I can to try and find this claim in anything by Glubb and failed.

I may have a way to get ahold of Forrest, in which case I'll likely submit another message, but it's hard to know if that's the case. In the meantime, I'm going to simply have to say this is not reproduced anywhere I've seen in any reliable fashion, and is at best a third-hand claim so far.

As for the Embassy in Amman, that claim is reproduced in Neff's book as well, and taken up by other books also quite unfavorable to Israel. It is clearly cited to a secret cable out of the US Embassy. However, the cable is not provided, and I've yet to see anyone cite how to get ahold of it. Even so, I think it's fairly undisputed that some bombing of civilians (and I will stress to be fair, neither side is innocent of this in that war, nor do we know the context of those bombings) had occurred. As to whether napalm specifically was used, I've yet to find a corroborating source or any indication of where the claim originates, or is reported or corroborated by anyone else in credible fashion. Hopefully I can get my hands on Neff and Forrest soon and get back to you on that, but without more corroboration of any sort, I think it's hard to trace this any further, and the lack of more information doesn't bode well for the likely accuracy of the claim.