Cognito - Azure AD - Amplify - flow of the SSO auth from application perspective

Without looking at your front-end code, it's rather hard to tell what Amplify SDK calls you are using to initiate the federated signin process. Basically, if you run a browser network trace, Amplify should trigger an /authorize call against Cognito UP to trigger the login flow. In order to do this from Amplify, you would typically call Auth.federatedSignIn() API call. Of course, this requites that Amplify configuration is setup properly where the name of identity provider, Cognito app client id, redirect uri are all properly set.

Typically, I initialize Amplify "oauth" Config with a OIDC/SAML backed idP as follows:

// AWS SDK & AWS Amplity Configuration
AWS.config.region = config.AWS_REGION;
Amplify.configure({
  Auth: {
    identityPoolId: config.AWS_COGNITO_IDENTITY_POOL_ID, // OPTIONAL - Amazon Cognito Identity Pool ID
    region: config.AWS_REGION, // REQUIRED - Amazon Cognito Region
    userPoolId: config.AWS_COGNITO_USER_POOL_ID, // REQUIRED - Amazon Cognito User Pool ID
    userPoolWebClientId: config.AWS_COGNITO_CLIENT_ID, // OPTIONAL - Amazon Cognito Web Client ID
    oauth: {
      domain: config.AWS_COGNITO_CLIENT_DOMAIN_NAME,
      scope: config.AWS_COGNITO_IDP_OAUTH_CLAIMS,
      redirectSignIn: config.AWS_COGNITO_IDP_SIGNIN_URL,
      redirectSignOut: config.AWS_COGNITO_IDP_SIGNOUT_URL,
      responseType: config.AWS_COGNITO_IDP_GRANT_FLOW
    }
  }
});

You can then invoke the idP based federated sign as follows, where the name of provider matches what you configure in your Cognito UP.

const { Auth } = Amplify;
// invoke amplify federated signin
Auth.federatedSignIn({
   provider: config.AWS_COGNITO_IDP_NAME
});

Hope this helps.