How do I log into my EC2 Linux Instance via Telnet Client?

There are no users with a pre-set password when an EC2 is initially stood up with an AMI.

To set one up, access your instance using SSH (or Instance Connect, or Systems Manager) as the default user - on Amazon Linux this is ec2-user

Elevate yourself to the root user sudo su -

Add a new user and set its password https://access.redhat.com/documentation/en-us/red_hat_enterprise_linux/6/html/deployment_guide/s2-users-cl-tools

Enter this new user's credentials and password when you telnet to the EC2.