There are a number of potential responses to this and it would be good to start with some exceptions to the question. I might look at the following issues:
- What defines 'modernism'? It is one of the more vexed and various of artistic movements, so much so that one of the leading critics on the movement, Peter Nicholls, believes that there is not necessarily a single coherent movement as a number of different modernisms (hence the title of his book Modernisms - I've included a link to a Google Books edition of the work so that you can do some reading around the subject).
- To claim that 'Modernism started in Europe' is itself a slightly complicated claim. Of course, it depends on which branch of the arts we are discussing but in literature, Henry James, an American, might well be see as one of the innovators of early modernist prose technique, albeit that he spent much of his literary career living in Europe. Equally, Virginia Woolf's famous essay, 'Mr Bennett and Mrs Brown' famously claims that 'on or about December 1910, human nature changed', a date she claimed was the inception of modernist art. This was the first meeting of the expatriate writers Ezra Pound and T.S. Eliot, both of whom were Americans. While many later critics have contested the date on which 'modernism' might started, most are in agreement that it emerged in a number of different places at different times. Nicholls, for example, sees some early signs of Modernist intention in Charles Baudelaire's Les Fleurs du Mal, in the 1850s. However, it is clear that in the early emergence of modernism as a literary form, Americans were very much at the heart of things.
- One might also look at the presence of Americans within Europe - to claim that the movement was 'started in Europe' but 'flourished in America' is, of course, too stark a distinction. When one moves from, what might clumsily be termed 'transitional modernism' (the earlier stage of modernism's development, such as when Pound and Eliot met in London) in to the period that most people think of as 'high modernism', a number of key Americans moved to America in order to be a part of the emerging European movement. Metropolitan centres of modernism emerged, perhaps most notably Paris among the expatriate Americans. Ernest Hemingway, F. Scott Fitzgerald and Gertrude Stein were perhaps most famous amongst the writers of this 'lost generation' of modernist writers working in Paris in the 1920s, alongside other European modernist innovators such as James Joyce and Pablo Picasso. One might look to Hemingway's A Moveable Feast as a later retrospective account of the influence of Europe upon an American's thought and artistic technique.
- It is, however, true that in some cases, American authors then returned to the USA and their art flourished from there, just as there were many American artists who did not ever go to Europe to learn of modernism. There are multiple reasons for this. Astradur Eysteinsson's influential work The Concept of Modernism posits the idea that modernism diverged in Europe towards two political extremes, communism on the one hand and fascism on the other, especially during the 1930s. However, one reason for the flowering of modernism in the USA during the 1930s and, indeed, in the period post WWII, was due to the absence of any large scale popularisation of political extremism. Indeed, this led to the emergence of an immigrant population of European artists and writers too - one only need look at writers like Nabokov or painters like Willem de Kooning to see this emigre culture being reversed. However, there were some Americans - one might think of Gertrude Stein or Ezra Pound - who remained in Europe, in the case of Pound due to considerable attraction to political extremism.
- Allied to this, as a country that has a proud history of welcoming migrants, the USA was, perhaps, particularly open to new influences from Europe and quite willing to adapt and innovate around these influences. New York, for example, has long been a melting pot of such cultural influences and, in late modernist works like, for example, Joseph O'Neill's Netherland, we can still see the site of a modern accepting city like New York, allowing the dialogue between these cultural discourses.
- A key facet of US development of modernism, however, also came down to both cultural and logistical circumstances. US education is not only excellent but based on a broad liberal arts tradition that allowed cross-pollination of ideas and the travel of people from and to different parts of a large country for study, disseminating modernist ideas to various cultural centres. Allied to this, as an emerging economic and political superpower, the communication system in the USA was especially well advanced, aiding the rapid spread of ideas. One further factor that might have influenced the later flowering and widespread development of modernist art in the USA might well have been 1944's GI Bill which allowed the returning servicemen from WWII to not only in many cases have experienced European culture but, moreover, to then return to a formal aesthetic education that then allowed them to articulate their own perspectives in the aftermath of the war and the ontological shock that it created.
This is, of course, to only give a brief response to an incredibly complex and interesting question.