I think that after Naruto obtained his father's half of Kurama's chakra, Minato's abilities (or at least some of them) were assimilated into his.
Thus, he learned FTG. Who better to teach him than the tailed beast who has been tamed by both Naruto and Minato? It certainly fits with a lot of ideas:
1. That the tailed beasts will be of great help to Naruto. We have already seen Son-Goku give Naruto the use of the lava element; if Naruto can use a Kekkei Genkai element all of a sudden, why can't he use a technique that his father created and that other people like Genma were able to learn?
2. Naruto surpassing his father. His Sage Mode surpasses Minato's, he surpassed him in the Summoning Jutsu, and he went above and beyond in a technique that Yondaime invented himself--Rasengan. Only FTG is left for Naruto to have completely succeeded his father in every aspect.
3. Having a weapon in his arsenal that Madara does not. The grandfather of the Uchiha and the second So6P has declared that he already has the powers that Naruto and Sasuke just recently acquired. Naruto's use of FTG might be the straw that breaks the camel's back in their fight against Madara. What would be more ironic than Naruto defeating Madara because of the same jutsu that caused Izuna Uchiha to die at the hands of Tobirama?
4. Vanity and the Surprise Factor. We will finally get to see Naruto really become the Yellow Flash. He will find some clever way to use FTG and everyone will be swooning over how fast he is, how clever he is, how unexpected it was for Naruto to use FTG that way, what a brilliant strategist Naruto is, yadda yadda. I personally can see Kishimoto doing this; it sounds like his style.
Just my 2 cents.