See my Fili and Kili essay for scene details. For clarification on how the eight functions work, see here.
Dominant Si: Fili spends most of his time watching Thorin. He is also traditional (he doesn't vote on Bilbo and he doesn't like elves) and not very spontaneous.
Auxiliary Fe: Fili has traditional morals (see above). He is also very in tune with the groups (and others') emotional state (passing ale around, his motivational speech at Bag End, watching the crowds at Laketown, etc).
Tertiary Ti: Ti is hard to see because it is both tertiary and introverted. However, we see hints of it in Fili's inability to understand Kili and Tauriel, and his speech to Thorin about leaving Kili behind.
Inferior Ne: Fili starts, and is an active participant, in throwing Bilbo's dishes around. He also wanders off with Kili when they are supposed to be watching the ponies.