The answer to this is complicated both definitionally (what do we define as "alchemy" and what do we define as "chemistry," and how do we tell them apart?) and historically (who do we take as "representative" of the body of work at any given point in time? how do we deal with outliers?).

We can certainly say that, by the time of the 18th century, scientists who dealt with chemical reactions considered themselves "chemists" and that they disdained any association with "alchemy," which they associated with mysticism, secrecy, and an obsessive quest for transmutation of elements. When we look back further, though, we find that alchemy was not just these things, and that it shared many common properties with what would later become "chemistry." And that there were sort of "intermediate" forms between the two, what historians today sometimes refer to as "chymistry" as a way to indicate that it was neither one nor the other.

So Robert Boyle, for example, is emblematic of the "chymistry" of this sort: he set himself in opposition to some parts of alchemy (the secrecy, for example) but at the same time he carried forward many other assumptions and practices of it (he replaced the mysticism with something perhaps a little more Christian at times, but he had essentially the same view of elements, transmutation, and so on as the medieval alchemists) even as he also pushed the work into a different sort of direction (more precision and documentation of experimental work, more clarity with hypotheses, etc.). He is sometimes cited as the "first chemist" and then, by other historians, as something like a "last alchemist," but even the latter isn't quite right as there were certainly people who would qualify as alchemists who survived him (like Newton). If one goes back further, one finds other "transitional" figures even earlier who have only relatively recently been getting recognized, like Daniel Sennert.

And going back even earlier, we find that, if you can cut through their jargon, a lot of the old "alchemy" is actually fairly decent chemistry, at least with regards to what was possible at the time. It wasn't just crackpots inhaling mercury fumes while they desperately tried to turn lead into gold; it was a serious observational and experimental "science" that did lead to some important discoveries and developments in human history, and had all sorts of tie-ins to other cultural realms (like art, religion, literature, etc.). There has been a "rehabilitation" of alchemy in recent decades among historians of science, in other words; it is not quite so silly or pointless as the 18th-century chemists caricatured it as being.

What we usually say is the "cut-off point" is the 18th century Chemical Revolution of Lavousier, Priestly, and Dalton, in which a lot of modern concepts and methods are sort of crystallized — including such basic notions as "there are a lot more than four or five chemical elements, and they are distinct from one another and cannot be transmuted into one another, and you can use all sorts of clever ways to separate them and look at and organize their properties," which is already a huge step away from the assumptions of chymists/alchemists like Boyle and Newton. But they of course were edged in that direction because of the transitional work that came before them.

Anyway, I think you get the gist of the answer: it wasn't a big, all-at-once sort of shift, but a gradual leaning, and you can find lots of exceptions at different places and time periods. But if you are looking for a simple mnemonic, it is not terrible to say, "in the 17th century, you start to see people doing things that look a lot more like chemistry, although they have not really renounced or rejected alchemy; by the 18th century, this moves even further away from some of the core concepts and methods of alchemy, and also they begin to define themselves by their lack of affinity with alchemy."

Much of the books of William Newman (Atoms and Alchemy) concerns this "shift" and the difficulty of even labeling it as a straightforward "shift." Lawrence Principe's The Secrets of Alchemy is also great if you are looking for more detail into what alchemy "was" — and how it was much more similar to what we consider "chemistry" than a lot of the stereotypes (Principe is part of a group of scholars who have gone to considerable lengths to reconstruct alchemical experiments, as a means of understanding the work more deeply).