Does the "butterfly effect" typify the slippery slope fallacy?

Not necessarily. A main tenet in chaos theory is that while deterministic, the effects are ultimately unpredictable . If we can accurately predict each step of the slope, it is just a "slippery slope" (no fallacy). If we can predict each step of the slope but the odds are ignored then it is a slippery slope fallacy. If someone claims that "because of the butterfly effect" you should not take a day off from work because it will lead to WWIII, then yes, that is fallacious and pretty much the slippery slope fallacy.