Adding KTN to Delta App
You can't add your KTN to the Delta app. You can only add it to your Delta profile on the Delta website. Here are the steps on how to do it:
Go to the Delta website: https://www.delta.com/.
Click on the "Sign In" button in the top right corner of the page.
Enter your Delta SkyMiles username and password.
Click on the "My Profile" tab.
Under the "Personal Details" section, click on the "Secure Flight Info" link.
Enter your KTN in the "Known Traveler Number" field.