If 18th-century scientists had been a bit stubborner and refused to give up on phlogiston, they might have gotten a jump start on electrochemistry.
Let's review the data that led to the phlogiston theory. It was based on the fact that when we see carbon burning, we see something being emitted, followed by the carbon losing mass. This was complicated by the fact that when we examine iron rusting, it gains mass. The phlogiston theorists tried dealing with this by assuming that phlogiston sometimes has levity instead of gravity. For some reason this wasn't taken seriously for long.
If the phlogiston theorists had been stubborner, they might have decided that the mass measurements merely located where the atoms are, not where the phlogiston is. If we assume that the oxidation of both carbon and iron involve the carbon or iron atoms giving up phlogiston to oxygen, it should be obvious that the combination of dephlogisticated carbon and phlogisticated oxygen went into the air whereas the combination of dephlogisticated iron and phlogisticated oxygen stayed solid.
In other words, in this theory phlogiston acts just like valence electrons.
Once scientists noticed there's a reaction when two metals of differing propensity to give up phlogiston came into contact, they might have realized that phlogiston was flowing. Experiments on the effect of trying to store the flowing phlogiston would have revealed that it's the same phenomenon as electricity. We might have started electrochemistry decades earlier.
But wait, there's more. Scientist would also have realized that the phlogiston particles had been labeled negative. This, in turn, would have corrected the guess that positive charges were marked by more atoms of electricity and led to less mental confusion among students trying to learn physics. (“What do you mean the electrons are flowing one way and the electricity is flowing in the opposite direction?”) We might have had more students taking physics courses, which might have led to additional benefits.