I did check first to see how much has been said about Alan Watts on the forum as a whole, with a decent search, before launching this post...
Earlier in this thread, Distrans wrote in 2013 that Alan Watts was probably an influence.
It'd be great if there were more direct evidence of that. Certainly it seems like they were both in California around the same time and both did radio work down there.
Comic Book Girl 19 (who prides herself on being 'Dune Lady' and hosts a book club every summer on the Dune books) posted Watts Wave 3 by Akira the Don on her Patreon Page, for Father's Day 2018. Which deals with Time possibly actually flowing backwards from the present instead of forwards, which was a key idea in the view of prescience in the Dune books (at least by the time Leto II takes the spice-essence in Children of Dune, and then forward from there).
Why else is this relevant? See below:
Anyway if you listen to the "watts waves" that Akira the Don has put on YouTube you can catch some of the references that are almost verbatim.
1. Compare in Chapterhouse Dune the jokes of ancient Dune about the wild desert ass going past the slit in the fence and the guy jumping up and saying the nose is the cause of the tail, with a spot in Watts Wave 3 (which deals with Time) except that Alan refers to a snake passing a fence.
[edit of 3-2-2019: the snake passing the fence is in Watts Wave 3 at 15:41:
https://www.youtube.com/watch?v=23pgfpgv_Pg
]
2. Compare in Heretics of Dune the quote where Taraza talks about "more damage has been done by reformers" with a spot about 2/3 of the way through Watts Wave 2 where Alan talks about a Confucius saying, the goody goodys being the thieves of virtue and how doing good to others and even doing good to oneself is amazingly destructive [edit: watts wave 2 at 23:31], because it's full of conceit.
[edit of 3-2-2019: the spot that most closely follows Taraza's chapter heading about damage from reformers is at 35:33 in Watts Wave 2:
https://www.youtube.com/watch?v=gH3eGosOqXU
]
[Between those two spots he talks about genetics which sort of presages the Tleilaxu stuff.]
3. Compare in Watts Wave 4 "What if we made a device that would give you anything you wanted? You would eventually have to make a button marked..surprise." and elsewhere "all perfectly known futures...are past. They have happened--virtually." with any of a number of points in God Emperor of Dune where Leto II says things like "a universe of surprises is what i pray for!"
[edit of 3-2

this is fairly early into Watts Wave 4, at 6:03:
https://www.youtube.com/watch?v=DhbAzFw-7xg
]
I will come back later and edit this post, and clean this up with actual minutes and seconds reference ranges to the videos, and page references in the books, assuming Freakzilla doesn't boot me off here for violating the No Advertising rule by mentioning either Comic Book Girl 19 or Akira's stuff (which could be construed as such I guess...).
Maybe he just meant no advertising as in no stupid banner links.
These were the first three, I suspect there is at least a 4th good piece of evidence in the Watts Wave videos that Frank had at least watched Alan's TV shows or listened to the audio of the lectures. Just can't think of it for now.