Martin Duberman has now published a very detailed biography of Lincoln Kirstein. Unless I missed something, I can't find the phase, or indeed any specific statement by Balanchine to Kirstein about this issue. In fact, despite the enormous amount of material that Duberman has utilized, there is actually very little he says about the interactions between Balanchine and Kirstein during the period in which the decision to come to America was made. (Balanchine takes up less space in Kerstein papers than one would imagine.)
Kirstein actually negotiated with an associate of Balanchine's, Vladimir Dimitriev (a former Maryinsky singer who had been instrumental in helping Balanchine Danilova, Geva and others out of the Soviet Union much earlier). Here's what Duberman says about the "school" aspect of their discussions:
Dimitriev, Lincoln wrote, felt that the project fell into two distinct parts: a school to train dancers and a ballet compan to perform; and at first "everything should be centered around the foundation of a school ... nothing at all should be mentioned about a company or ballets"; it was essential "to emphasize the non-commercial aspects of the venture."
I assume that the idea of a school was indeed part of what Balanchine had, either vaguely or specficially, in mind. And, certainly, Balanchine must have had quite a number of ideas and aspirations floating through his head at the time he was considering risking a move to America. However, shortly after his arrival in New York City in 1934, he came down with what was either a recurrence of tuberculosis or some sort of pneumonia. It was the highly opinionated and truculent Dimitriev who worked with Kirstein on the arrangements for coming to America. Once here, he was the one most involved (with Kerstein) in incorporating of the school, finding the location for its first studio, organizing the lease, hiring the staff, and even obtaining students.
Balanchine -- at least in Duberman's version -- seems to be something of a phantom figure in all of this. It's the absence of Balanchine's guidance, direction, and even physical presence which is most striking about the foundation of the School of American Ballet. At least as reflected in Kerstein's own papers.
So where did the idea -- let alone the wording -- "But First a School" come from?
Bernard Taper's 1984 biography Balanchine certainly perpetuates the idea that "first a school" was at the heart of Balanchine's plan for ballet in America.
There are no footnotes in Taper's book, so it's not possible to find his source for this. Most probably Taper drew from one of Kerstein's later memoirs, written with the benefit of knowing that both school and ballet company were enormous successes.. The Balanchine we find in this material is a huge and somewhat enigmatic spiritual presence, a visionary if not a prophet -- a man who "knows" and acts on that knowledge.
Fervently, Kirstein promised Balanchine that by the time he was forty he would have a company and a theater of his own. Balanchine replied, "But first a school."
Duberman, on the other hand, relies on Kerstein's own diaries and other sources produced at the time the events were occurring. Balanchine appears to be -- as one might expect -- rather confused by these events, alternating big dreams and a rich menu of anxieties. In this version, he's a human being, not a prophet nor an icon-to-be, an understandably conflicted man, suffering from a recurrence of a serious disease, and literally or figuratively "absent" when much of the planning was done. In all of this, "a school," while definitely part of the plan, is just one of a number of arrows Balanchine is shooting into the air.