babaganoosh13 got me sorted, but I thought I'd outline my problem for future reference.
In the training for Nagasaki, you hold the right stick down and rotate the left stick until it vibrates and when prompted, push the right stick up to release the fart.
In the field, you press the right stick down then up and you hold it up while rotating the left stick until it vibrates and when the screen shakes you let go to release it. Now, the screen prompt does say to push the right stick up, but it doesn't say anything about pressing it down first. When I tried just pushing the right stick up, my character just did a tiny fart, even if I held the stick in place.
That's the issue in a nutshell. Do with this info what you will. This was my only real problem with the game, other than that, it was wonderful.