How an employee can handle conflict instructions at work from two superiors whom are in power struggle ?

This definitely is a very uncomfortable spot to be in. The primary thing for the employee is to ensure that he doesn't get entangled in the conflict of his superiors. His focus must be fixated on the job at hand and his documented Job Description. It often helps to request a clear reporting line from his documented boss and take it forward from there. As a safe measure, the employee may request the senior outside his reporting line to assign any work to him through his direct manager by following proper channel!