Steps for get PRIVATE API KEY:

Step 1: Login to your Klaviyo Admin Portal. Klaviyo Portal

Step 2: Go to your Klaviyo account, click on your username and choose Account And Click On Settings.
Reference image

Step 3: Then choose API Keys from the drop-down menu.And Click On Create Private API Key.
Reference image

Step 4: Give name to API key ,click on Full Access Key and Click on Create button.
Reference image

Step 5: Copy the Private API Key 
Reference image

Step 6: Paste in below text field.

Step 7: Click on Verify button.