API calls will either be made programatically or through a rest client app. It cannot be made through a browser because by default a browser does not allow you to pass headers. The invalid headers error/ authentication error is seen because the HTTP headers are not being passed.
To make the call through bash shell -
curl -H "Fk-Affiliate-Id:<your tracking Id>" -H "Fk-Affiliate-Token:<your token>" "https://affiliate-api.flipkart.net/affiliate/offers/v1/dotd/json"
You can get the affid and token from this page on the affiliate dashboard https://affiliate.flipkart.com/api/api-token
To make a call through a rest client -
You can install a google chrome browser extension like postman. And make a request as in the screenshot attached.