Duplicates not allowed if I'm trying to link TestComplete tests and Zephyr Tests

Sounds like that test has already been linked to another test item in your Execution Plan. You cannot link a single Zephyr test to more than one test item in TC. However, you can add more than one Zephyr test to a single test item in TC, provided the Zephyr tests have not already been linked. 

I also don't see any Jira items selected in your 'link external cases' window - did it disappear after you clicked Finish? I assume you have already set your project properties in TC to reference your Jira project and tested the connection?