This is shown in "Ocarina", "Wheels", and "The First Investigation", when he interacts with Kim Kil Whan.
None of the pups really refer to him as their uncle, possibly due to some of them acting more mature than Finn due to their early adulthood.
But, in the end of the episode, they go back to being friends again after their confrontation with the Dream Warrior. ", when Finn is seemingly hurt by the fact that Ice King could so easily drop his lifeless body, Jake consoles Finn by saying that if he came across Finn's lifeless body, he would clasp Finn dramatically for a "kajillion" years. ", when Finn and Jake compete to keep silent the whole day, only communicating with written signs, Finn was not able to carry out a normal conversation with the signs he had written. Their close friendly and brotherly relationship is also displayed when Finn shows the sign "I Love You, Jake" when he was angry at Jake, and shows the sign "Jake Rules! In the episode "Dungeon Train", Jake shows genuine love and care for Finn, going as far as to promise to stay on the train with Finn, despite this being against Jake's wishes.
But this really upset Finn, not wanting to lose his brother.
In the end of every bout or argument, they always reconcile, however.
In "Who Would Win," Finn and Jake actually fight each other physically, after Jake won't take training seriously and the ensuing fight caused multiple injuries to both of them.
However LSP managed to get Finn and her out of the slime.
After Finn became motivated to save Ooo even more with the idea of saving Jake.
In Goliad, Finn and Jake were saved from Goliad by Stormo.