Peter might be initially very nervous. He's been keeping this huge secret from Aunt May for a long time, and now that it's out, he's worried about how she'll react. He might stutter and struggle to find the right words to explain himself.
She might also be a bit angry that he didn't tell her earlier. She could feel left out or betrayed that he kept such a big part of his life from her. This could lead to some tension between them for a while until they work it out. She might make him promise to always be honest with her from then on.
She could also be very proud. Peter is a hero as Spider - Man, and Aunt May has always known Peter to be a good person. Now that she realizes he's using his powers for good, she might see him in a new light and be proud of the man he's becoming.
Peter could be really nervous at first. He's been keeping this huge secret and now it's out. He might stutter and try to explain himself, saying he was just trying to protect her.
Their relationship could become more strained. Aunt May might feel betrayed that Peter kept this big secret from her for so long. She might question his trust in her and this could lead to some arguments between them.
She might also be proud in a way. Peter is a hero as Spider - Man, and Aunt May has always known Peter to be a good - hearted person. Once the initial shock wears off, she could see this as an extension of his kind nature. She might start secretly helping him, like making sure he has proper meals and rest when he comes home tired from his Spider - Man duties. And she could be a great source of emotional support for Peter, which he really needs in his double life.
She might also be proud. Peter is using his powers to help people, and Aunt May, being a kind - hearted person, would likely be proud of him for that. She could start to brag about him to her friends in a very discreet way, of course. And she would probably be more worried about him than ever, constantly thinking about all the risks he takes every time he goes out as Spider - Man.
Maybe in the fanfiction, Flash discovers Peter's identity in a very unexpected way, such as seeing Peter's Spider - Man suit by accident. He then has to decide whether to keep the secret or not. He might struggle with his own jealousy towards Peter and the newfound knowledge. If he decides to keep it a secret, it could lead to an unlikely friendship between them, with Flash helping Peter in small ways without Peter knowing it's him.
Well, it could lead to a lot of chaos. Maybe she'd be shocked and try to put a stop to whatever wild situation was going on in the fanfic. She might start lecturing the characters involved, especially if it involved something she thought was inappropriate or dangerous.