To my mind, it must be acknowledged that thinking of what makes someone an American poet (or an American anything) is to think in clichés. I don't mean to say it's a meaningless endeavor or that those clichés are utterly off-the-mark. I just think a key way of considering myself an American poet entails conglomerating a number of truisms about what America means. This would be true of any effort to describe the kernel of one's place in a discourse that is national, regional, identity-based, etc. In other words, I am an "American poet" insofar as I have been shaped by (and even embrace) many of the aspects I associate with the American episteme. For me, most of these forces feel like sites of trauma (or trauma's residues). In a phrase, I am an American poet because I was born here, and I lived here, subject to some unique mixture of cultural strains native to this place.
I was raised in the Southeastern United States where clichés about bigotry (racial, religious, sexual) are often painfully true. I was educated in private schools where clichés about American ambition and ruthlessness are often painfully true. I was conditioned by a roil of pernicious and salutary social projects (deeply engrained double-standards favoring wealthy-straight-white men challenged in the most substantial way ever by equal rights movements and philosophies).The hyper-confusion of eros and commerce often associated with the deep puritan strain holds me enthralled. Shame. American Shame, which is always as productive as it is internal and catatonic, makes me an American person at a certain point in history, and by extension it makes my poems.
As far as the "specifically American" features go, I have to say I think the specificity is to be found in the arrangement of what are really general features of human experience. Again, the clichés about the tensions or traumas that have defined American culture point at something real and inescapable. I would say the same thing about American painting or film. So, yes, I believe it is as reasonable to categorize poetry as "American" as it is to categorize any other art form in that way.
In the broadest sense, I don't think there is anything formally distinctive about American poetry. It is organic, and every organism is distinctive in its way [no two snowflakes being alike, etc.], but I don't think we can look at the idiosyncrasies of organic development and then make an inductive leap to anything American about those idiosyncrasies [e.g., "these are American snowflakes because no two are alike"]. We're stuck with approximate, received notions about what is American from which we can really only hope to make comparative measurements.
The American poetic tradition seems pretty capacious to me, but that also stems from a host of clichés about American omnivorousness. It's a privilege of empire to assimilate treasures from conquered lands (are the Elgin Marbles English? What about Keats' poem about them?). It's hard to imagine "my tradition" without all kinds of influences from Europe, South America, Africa, Asia, but I don't consider the stream of input to be unmediated or "natural." Instead, the international influence is present insofar as it has been natural-ized. Translated into English, generally by American poets, into the American storm. There's usually even shame in this. The shame of requiring a translation (both in the linguistic sense and in a more thematic sense [viz. the shame of needing a transfusion of cultural authenticity]).
Ultimately, for me, the important American thing is its self-absorption (another cliché). Much of what makes American poetry American is one or another kind of preoccupation with the internal frictions that have propelled and continue to propel America as a nation, a population, a culture, an idea. But it isn't just pre-occupation with those frictions; it is also implication in them. So, one necessary (although not sufficient) feature of American poetry is that it comes from inside the American self, and another is that American poetry reflects that American self. All of this feels beleaguered and on the way out, but it also feels lucky and redeemable. American poetry is filled with sin, and it knows it. Maybe American poetry has also already been saved by forces beyond the scope of its short sight.