"Enough! You should NOT toy with the emotions of a fire elemental!" - Flame Princess
She develops a crush on Finn the Human after Jake the Dog courts her on his behalf in "Incendium," but Jake rescinds the offer after her father the Flame King pronounces her as his "evil" daughter and she shows a firey temperament. She angrily chases Jake to where Finn and Jake live and sets fire to their Tree Fort, incurring Finn's wrath after she destroys his Princess Bubblegum photos in the process. He follows her to the roof and discovers her true nature, and though she slaps him and leaves a burn mark on his face as she departs, he develops a crush on her.
In "Hot to the Touch," Finn and Jake pursue Flame Princess to a lake, where they learn that putting out the fires she sets harms her; Finn nevertheless calls her beautiful and wants to spend time with her, causing her to glow brightly, both literally and figuratively. Because he defensively puts some of her flames out, she thinks he came to impede her so threatens to burn down a village. Finn and Jake attempt to save the village using fireproof suits, but when their attempt fails, Finn breaks out of his suit and starts crying. Flame Princess notices this, puts out the fires, and calls him a Water Elemental because he produces water by crying. She is impressed that he "would defy nature" to be with her, so they hug, burning him in the process. Their relationship has begun.
In "Burning Low," Flame Princess and Finn are dating and successfully hug after Finn is wrapped in several layers of aluminum, and Jake advises him to take their relationship to the next "tier" - kissing. Princess Bubblegum, upon learning of Finn's new love interest, attempts to warn Jake scientifically about the effects of such a kiss, but he dismisses her as being jealous. Finn and Jake separately tell her how Finn had been in love with her but has moved on; finally, she tells Jake in simple terms that, if Finn kisses Flame Princess, she'll burn the entire earth from the inside. Jake and Bubblegum arrive too late to stop the kiss but succeed in blocking the hole caused by the resulting explosion, depleting the oxygen supply and stopping the reaction at an early stage. Finn stabilizes Flame Princess with another kiss, and after Jake returns them to the surface, they each kiss a rock to safely confirm their mutual love. She has since committed no further evil acts, and it is stated that in the upcoming 2012-2013 season of Adventure Time she will return to redeem herself, which would complete the transition from anti-heroine to tritagonist.
In "Frost & Fire", Finn tries to get her and Ice King to fight by lying in order to complete his dream. This, however, leads to Finn attempting to apologize and to continue their relationship, but to no avail as Flame Princess leaves Finn saying "I need some time alone." However it doesn't mean they broke up... as we are quite sure Finn can fix it.
In "Earth & Water," Flame Princess overthrew Flame King and became the new ruler. When Finn tried to apologize to her, she accepted his apology. He asked her if they were still going out, she said no and told he that she need to stay to rule her kingdon. However, they could still be friends and that he can come by anytime as long as he is completely honest with her.