One thing that Pennsylvania (world 2 level 1) and Illinois (world 3 level 1) have in common is that they have an area where enemies with an AI similar to the hammer bro from Super Mario Bros will throw torches and jump around on a set of two floating platforms.

In Pennsylvania, there will be a staircase seemingly identical to the staircases before the end of most levels, but the level will not end here. Fall off this first staircase without jumping, and without hesitation, continue running, and run on the grass under the platforms. If you did not hesitate, the flamethrowers should be jumping on the second platform, with their torches high in the air. Do not jump onto the second platform, you will be hit by the flamethrowers or their torches.

In Illinois, you'll eventually come to a tiny staircase followed by three platforms with paratroopas in between them, which you can easily clear. This is a zero hesitation situation, so do not let go of the run button, keep holding the joystick towards the right, and as soon as you see floating purple bricks, jump on them. If you correctly avoided hesitation, the flamethrowers should be on the grass and their torches should be high in the air, with you in the middle. Do not continue to run on the grass like in Pennsylvania or you will get hit or fall to your death. An easier way to do this is to jump onto the purple bricks, but immediately turn around and jump onto the highest platform.

Additionally, you will encounter one other flamethrower towards the end of Illinois after a tiny staircase leads to two narrowly spaced out floating platforms. The trick here is once again zero hesitation. Keep running don't jump, and the flamethrower will jump over you. There will also be a flamethrower in Kentucky, which you can easily avoid by not hesitating and going either under or over the platform.