Finn/Flame Princess: This relationship is currently in full swing. And it IS very cute, its fantastic to see Finn be happy, did I mention its cute? Cute. Flame Princess is adorable.
I think the relationship is presented to be temporary though. FP doesnt really have much happening other than her relationship with Finn, and her limited traits. She has some anger issues, which would come with being made out of fire, shes evil and could possibly turn good, and thats about it.
If you look at the way FP was introduced into the series, she was completely portrayed as a replacement for PB, as far as Finns affections go. Jake went out to find someone else for Finn to like. FP showed up asking Finn if he liked her. Flame Princess already liked him, possibly since he was the only way she could have escaped the lantern. FP presented herself in a romantic way right after Finn was completely distraught over his feelings for Bonnie. Finn has not really known FP in any way other than a romantic interest. The relationship has even somewhat been pushed on him by Jake. Its almost as if Finn had no choice but to fall for FP. It was easy.
And ever since they got together, there hasn’t been any talk of ‘Ill be with her forever!’ 'Flame Princess and I will be just like you and Rainicorn!’, there hasn’t been any suggestion that this relationship is forever. Don’t all young teens think their first relationship will last forever? Instead, we just get Finn saying he has to keep Bubblegum interested in case 'this Flame Princess thing doesn’t work out’. All the Jay T Dawgzone stuff. He puts miniPB in between miniFinn and miniFP to break them up in All the Little People. It seems like Finn knows he wont be with Flame Princess forever, which isnt too promising for a budding relationship.
Even though Finname is absolutely adorable, it really is just a distraction from Finns crush on Bubblegum, and a way for Finn to mature with his view on relationships. It wont be endgame.
I’m much more interested to see how and when they break up, and what effect will this have on both parties. Will Bubblegum be involved? Will Finn grow a lot from it? Will Flame Princess and Finn remain friends? I hope so, shes cute.
FP has also been set up to be evil. She did burn a lot of stuff, she can potentially destroy the whole planet, and her father seems to be pretty manipulative. I have a theory that the Flame King is going to convince FP to be evil again, and Finn will be conflicted, trying but failing to turn her to good and justice. Maybe she will try to get revenge on Bubblegum for locking her up, and Finn will reluctantly choose to protect PB over helping FP. That would be pretty dramatic.