Maybe Artemis figures out where he is. She has her own set of skills and knowledge that could lead her to the island. Once she arrives, she and Dick work together to get off the island. For example, she could have some knowledge about the tides that helps them build a better raft for their escape.
One possible scenario in such a fanfiction could be that Dick Grayson gets sick due to overexertion during a mission. He might be pushing himself too hard to prove his worth to the team. His sickness could then lead to other members of the Young Justice team having to step up and take on more responsibilities, which in turn could develop their characters further. For example, Wally West might have to take over some of Dick's leadership roles and learn to be more patient and strategic in the process.
His identity crisis is also a frequent theme. As Dick Grayson has multiple identities such as Robin and later Nightwing, fanfiction often explores how he balances these identities, especially when he was young and still figuring things out. There are stories that show his internal struggle between being a normal kid and a crime - fighter, which makes for really interesting reads.
One possible fanfiction could involve Dick Grayson getting angry when his team in Young Justice makes a decision without consulting him. He might feel that his leadership skills are being undermined and this could lead to a big argument within the team.
One common theme is the development of their relationship. Whether it's a friendship or something more, it often evolves over the course of the story as they face different challenges together in the Young Justice setting.
One great Dick Grayson Young Justice fanfiction is 'The Robin's Journey'. It focuses on Dick's growth within the Young Justice team, exploring his relationships with other members like Wally West. Another is 'Grayson's Leadership', which delves into how he steps up as a leader in various challenging situations. And 'Dick Grayson: Beyond the Mask' is also good as it shows his life outside of the heroics while still being connected to his role in Young Justice.
The plot could be that Dick Grayson gets angry when a new member is brought into the Young Justice team without his approval. He might think that the new member has a hidden agenda. So, he starts to investigate on his own, causing tension within the team as they think he's being paranoid.
One interesting plotline could be them having to deal with a new and powerful villain that specifically targets their relationship. For example, a villain who tries to turn them against each other by manipulating their past traumas. Another plotline might be them training a new group of young heroes in Young Justice together. It would show their different teaching styles and how they complement each other.
One possibility is that Dick has to use his survival skills learned as a hero to find food and shelter. He might also encounter some strange creatures on the island that he has to either fight or outwit.
Some Tumblr blogs are also dedicated to sharing and discussing fanfiction. Search for tags related to young Dick Grayson fanfiction on Tumblr. You might find some hidden gems there, as well as get recommendations from other fans.