First, understand the characters of Nightwing, Batgirl and the Young Justice universe. Read the official comics and watch the shows related to them. Then, come up with an interesting plot, like a new threat they have to face together.
One great 'nightwing batgirl young justice fanfiction' is 'The Young Justice Reunion' which focuses on the dynamic between Nightwing and Batgirl within the Young Justice universe. It has a lot of action and great character interactions.
One idea could be that Nightwing has to train the Young Justice team in some new combat techniques. Maybe there's a new threat in Gotham that requires their combined skills to take on. Another could be a time - travel plot where the Young Justice team gets sent back in time and meets a younger Nightwing, and they have to work together to get back to their own time. Or perhaps Nightwing goes undercover in Young Justice to investigate a mole, leading to a lot of mystery and drama within the team.
Definitely the interaction between Nightwing and Robin (from Young Justice). Since Nightwing was once Robin himself, he could offer a lot of wisdom and guidance to the younger Robin. Also, the interaction between Nightwing and Artemis would be great. They both have a lot of combat skills and a bit of a sarcastic side, so their banter would be really fun to read. Another interesting one would be Nightwing and Superboy. Superboy might look up to Nightwing as a more experienced hero and Nightwing could help Superboy better understand his powers and his place in the hero world.
Sometimes, an old enemy of Nightwing might resurface and take on the Justice League as a way to get to him. For example, a crime lord from Nightwing's past who has amassed new and dangerous technology and uses it to take down the League, thinking that Nightwing will come running to save them.
A potential storyline could be Nightwing joining the Justice League on a trial basis. He has to prove himself to the more established members. This could involve a series of missions where he showcases his skills in detective work, combat, and teamwork. Another storyline could be Nightwing being wrongly accused of something by the Justice League, and he has to clear his name while also dealing with the threat of a common enemy.
One possibility is that Nightwing brings his unique set of skills and street - level experience to the Justice League. He might initially be seen as an outsider by some members, but his charm and combat abilities would quickly earn their respect. For example, he could offer new strategies for dealing with villains who operate in the shadows of cities, which the more powerful but sometimes less street - savvy League members might not have considered before.
You can try fanfiction websites like Archive of Our Own (AO3). It has a vast collection of fanfictions, and there's a good chance you'll find some related to the Justice League and Nightwing there.
One plot could be that the Justice League realizes they need Nightwing's unique skills in stealth and detective work to solve a mystery that has stumped them. Maybe there's a villain who is always one step ahead, and Nightwing's street - level experience can give them an edge.
One interesting plot point could be Nightwing using his unique acrobatic skills to outmaneuver a powerful enemy that has the Justice League trapped. For example, he might swing through a complex maze - like structure created by the villain to reach and free his teammates.