Thanks to the guideline by @identigral I have managed to obtain the callback URL by using the following approach - here Sample_Auth is the developer name for the Auth Provider
String ssoUrl = Auth.AuthConfiguration.getAuthProviderSsoUrl(null,null,'Sample_Auth');
String callbackUrl = ssoUrl.substringBefore('/auth');
callbackUrl += '/authcallback/Sample_Auth';
I found this can also be achieved with help of the URL class, which is much easier to work with.
String baseUrl = URL.getOrgDomainUrl().toExternalForm();
String callbackUrl = baseUrl+'/services/authcallback/Sample_Auth';