Dear JWilliams1219,
Good day! Thank you for posting to Microsoft Community. We are happy to assist you.
Based on your description, Teams will flicker non-stop when joining a meeting from the Outlook calendar if Teams is not already open.
As you mentioned the issue happens for more than one user, this should not be a specific client issue and clearing MS Teams cache doesn't fix the issue. Since the issue is difficult to reproduce from our test environment and it seems more complex than that we can handle, we suggest you contact the higher-level support for more professional support: Please (use the admin account to) go to Office365 admin center>Support>New Service Request. The support engineers there have the correct escalation channel, and this is the most efficient way to report such issue. You can refer to this article to check the way how to raise a ticket: Ways to contact support for business products - Admin help. The engineers in related team have higher permission and resources than us to help check the root cause from background directly, they can also use remote session to connect to your environment to check for you if necessary.
I hope the information can be useful and you can get better support from the higher-level support. If there is any update or I misunderstand you, please feel free to let me know. I will continue to assist you. Your understanding and co-operation are highly appreciated.
Thanks for your precious time. Have a nice day!
Sincerely,
Sherry | Microsoft Community Moderator