In a fanfic, their relationship could be developed through cultural exchanges. Since Jake is from Ooo and Lady Rainicorn is from the Rainicorn Kingdom, they could introduce each other to their respective cultures. Jake could learn about the Rainicorn language and traditions, and Lady Rainicorn could experience the unique things in Ooo like the slime pools. They could also have joint hobbies like creating art together using Jake's stretchy powers and Lady Rainicorn's ability to write in the air with her horn. This would bring them closer and deepen their relationship.
One way is to show them sharing their secrets. Lady Rainicorn could tell Jake about her family in the Rainicorn Kingdom and Jake could share his dreams for the future. They could also have arguments over small things like what to have for dinner, which shows their closeness and comfort in being honest with each other. Then, they make up and their bond becomes stronger. Also, they can protect each other from danger. When Jake is in trouble, Lady Rainicorn uses her horn's powers to save him and vice versa.
A cool plot could be that Jake and Lady Rainicorn discover a hidden dimension. In this dimension, they find out that there are versions of themselves with different powers. They have to work together to find a way back home while also learning from these alternate versions. Or perhaps a story where they are invited to a royal ball in the Candy Kingdom but end up getting caught in a mystery involving a missing jewel. They then use their unique skills to solve the mystery.
A good way to develop their relationship is by introducing a conflict that they have to resolve together. Maybe there is a misunderstanding between them that leads to a rift. But as they work through it, they realize how much they value each other. They could also have moments of vulnerability, like Finn sharing his fears about not being good enough, and Huntress Wizard sharing her insecurities about her magic abilities. This would make their bond stronger.
Another way is through music. Since Marceline is a talented musician, she could teach Ice King how to play an instrument. This shared activity would be a fun way for them to bond. As they practice together, they would get to know each other better on a more personal level. It could also lead to them creating their own unique music that reflects their relationship and experiences.
Their relationship could develop through shared hardships. For instance, if the kingdom is under attack and they have to hide together. Cinderella's kindness during this time might make Lady Tremaine question her past actions. Another way is if Lady Tremaine gets sick and Cinderella takes care of her, slowly breaking down the walls of hatred.
Another possible theme is the exploration of different cultures within the Adventure Time universe. Lady Rainicorn comes from a different species, and fanfictions can delve into how her culture and Finn's human - like culture interact and influence each other.
In the fanfic, their relationship could be developed by putting them in situations where they have to make sacrifices for each other. Maybe Finn has to give up a chance at a great treasure to save Huntress Wizard, or Huntress Wizard risks her magic to protect Finn. These selfless acts can make them realize how much they mean to each other. Also, they could have simple, everyday interactions like cooking together or sharing stories around a campfire that slowly build a bond between them.
Finn might initially go into denial. He could keep expecting Jake to just pop back up like he always does. Then he'd probably get angry, at himself or at whatever caused Jake's death. Eventually, he'd start to accept it and try to honor Jake's memory by being a better hero.
Finn would probably be very protective. He might stand guard outside her resting place and keep a lookout for any potential danger. Jake, on the other hand, could use his shape - shifting abilities to make things more comfortable for Lady Rainicorn, like creating soft beds or warm blankets. Princess Bubblegum might use her scientific knowledge to make sure Lady Rainicorn has a healthy diet and proper medical care.
One interesting fanfiction could be about Finn and Lady Rainicorn going on a magical quest together. They might encounter strange creatures and have to use their unique skills to overcome obstacles. Finn's bravery and Lady Rainicorn's flying ability would be really useful in such a story.
Their friendship could be developed by having them share secrets. For instance, Marceline could tell Jake about a time she was really scared as a vampire. Jake, in turn, could share his fears about losing his family. This would deepen their bond.