Also ran into the same issue trying to patch zoom.
I reached out to Zoom support to look into this and they had suggested this was a Mac problem but that an uninstall/reinstall would resolve the error message. 
Been noticing this issue anytime we deploy Zoom to any machines with the Big Sur OS (both intel & m1s). Seems to only happen when Zoom gets installed the first time, but doesn't happen when we push out a Zoom update (for now).
Just a quick update to this, I also reached out to Zoom in desperation and they told me it was a known issue. Ever since Zoom 5.6.3 my issue appears to be solved on Intel machines but not on our M1 machines. Unfortunately we do not have enough M1 machines to test effectively, but otherwise my issue is resolved!
It looks like this just randomly started to happen in my environment. Affecting both M1 and Intel machines. It's weird that this keychain message only comes up when installing Zoom through JAMF. When you manually install Zoom, the message doesn't come up. I tried pushing out an older Zoom pkg, but after it installs, a popup comes up asking if the laptop wants to allow Zoom to access the downloads folder, after hitting yes, the keychain message comes up.
Edit: Pushing out the Zoom IT admin pkg seems to work. I deployed to 3 laptops and no keychain message comes up.
Can we turn off the keychain for this app since we are also running into this issue with the M1 & Intel Mac Pro's & Intel Air's.
I have been getting this as well. It's random. Does anyone have a fix for this?
Happened to me on an Intel MBP. Again. Seriously, will we need some public embarrassment episode with potential liability so JAMF starts to take this seriously? 🙎
I was able to follow the tip from user-VwlRMRYoow and get it to work on my 3 test Macs. An Intel, M1 and M1 Pro running Big Sur, Monterey and Monterey respectively. I create d a patch policy with the IT version rather than the regular version and it deployed to all three Macs automatically with no keychain prompts.
You can get the IT Installer version from Zoom's downloads page here:
https://zoom.us/download
(Look in the blue bar at the top of the page)
You can also get some tips on deployment with a preconfigured plist file that will let you configure the client a bit more from here:
https://support.zoom.us/hc/en-us/articles/115001799006-Mass-deployment-with-preconfigured-settings-for-Mac#h_9f50f97d-e769-4a47-a2b3-1f64efc670df
ZoomInstallerIT.pkg worked for me as well. Thanks @VintageMacGuy
+1 for @VintageMacGuy 's solution. I tested it thoroughly on the latest two versions of Zoom and this seems to have solved my issues. I will mark it as the solution to the thread. Thank you!
this issue seems to be popping up again I have been using the IT zoom for admins pkg for a while now, from some reason seems to be very random we do have most of our users on SSO and one a few have user passwords anyone else starting to get his message again?