I've looked into the history of the phrase 'critical thinking'. Given the phrase's Kantian connotations, it's no surprise that several early uses of 'critical thinking' occurred in papers about Kant. For example, there are a couple of uses in an 1883 issue of the Journal of Speculative Philosophy, which was prepared (a couple of years earlier?) to mark the 100th anniversary of the Critique of Pure Reason. (One use is on p. 232 of an English translation of a paper by Kuno Fischer.)
There are even earlier uses in some American, Protestant religious publications, which are also likely to have a Kantian source.
As the Google Ngram at the end of this post indicates, use of the phrase took off in the 1890s. What sparked its surge? It might be the use of 'critical thinking' in the 'Art of Thinking' (c. 1892) by Henry Makepeace Thayer. That piece found its way into a school textbook (Ethics of Success: a Reader for the Higher Grades of Schools, 1894).
Some authors show a tendency to use interchangeably the phrases 'critical thinking' and 'reflective thinking'. Both phrases have a Kantian ring. The Kantian aura is clear in George Trumbull Ladd's 1904 Presidential Address at a meeting of the American Philosophical Association. Ladd spoke of philosophers as 'reflective and critical thinkers' ('The Mission of Philosophy', The Philosophical Review 14 : 119) and of philosophy as resting on 'critical and reflective thinking'. (Ibid., 120, 126, 135) A big part of Ladd's paper focused on Kant. Accordingly, Ladd gave a Kantian characterization of philosophy as being addressed not directly at external reality but, instead, at our cognitions or representations of that reality. Ladd, himself, was much influenced by Rudolf Hermann Lotze and was familiar with the works of German philosophers and psychologists who followed in Lotze's wake (e.g., Wilhelm Wundt, Benno Erdmann, and Christoph Sigwart).