Tracking clicks for an external tool in Klaviyo campaigns

I think that will be a question to your analytics tool rather than a question regarding klaviyo. The click tracking within klaviyo solely depends on what is happening while people interact with your emails. And here it doesn’t make a difference if you link to an url in your shop or to an extern url. If someone clicks something in your email the click will be registered and utm parameter will be added (if enabled). 

Obviously when you link to an external site that you don’t have Google Analytics access to you won’t see any data in your own Google Analytics account. So you will only see the clicks on that email to that external url in the link activity tab.