There's a scene where Jimmy is supposed to get a flute from a farmer, and you're required to skip a cutscene in order to stop Jimmy's stuttering. However, this seems to be the only time in the game where I'm unable to skip the cutscene. Holding the B button doesn't work.

You're not "required", he'll eventually get it.

Give him time.

Hmmmm… I guess I'll have to give him a chance, then. Maybe you did that on purpose and the mission is to wait for him to finish speaking.

You have to wait it out. It's not skippable just like *spoiler* at the very end when the Govt guy starts talking and says "oh your not gonna wanna skip this".