What should she do in this situation? 

Back in the day, office romances were much more common. A ton of people met their future wife or husband at work, but this method of matchmaking has decreased over the past 50 years for several different reasons. People’s social lives are much less intertwined with their work lives than they used to be. It’s much more common for employees to go to the office, do their work, and leave without ever taking time to socialize with their coworkers. There are some offices where coworkers go out for happy hour Monday through Friday, and all of their coworkers are their best friends, but that is more the exception than it is the rule. If coworkers can’t even find the desire to be friends with each other, there’s literally no way they’re going to date each other. 

Another reason coworkers are unwilling to date each other is that harassment policies can be somewhat unclear about what constitutes workplace harassment. They usually define harassment as making unwanted advances, but how are you supposed to know that the advances are unwanted until you make them? One employee might see unreciprocated flirting as harassment, while another might reciprocate the flirting, start a relationship with the flirter, and get married to them! It all depends on the person, and most employees would rather not risk their careers by flirting with coworkers if they think it might get them in trouble. 

The manager in this story has not reciprocated her direct report’s flirtatious behavior. He’s clearly not getting the message that she’s not interested in him in this way, and she doesn’t know what to do about it. He hasn’t asked her out, but he clearly has a crush on her.