I think it's safe to say that this is absolutely a trick question. Emily Dickinson and Walt Whitman are most certainly NOT the founders of poetry! Heck, they are American poets and the United States has only been around for just over 200 years! Poetry has existed long before the United States, ... and will exist forever after the United States is long gone!
Meanwhile, the actual writer of "The Seafarer" in ancient England is rolling over in his grave, ... and so are the ancient scops that spouted their poetry orally.
Putting my disgust aside for a bit, though, ... it is an interesting idea in itself because both Walt and Emily are two poets that focus on personal exploration, ... mostly exploring life and death respectively. I'm not sure there were two poets that limited their subjects in that regard quite that exclusively, I suppose. In addition, it is interesting to consider that both of them lived quite solitary existences. That is a similarity as well. Not enough to declare them the "founders of poetry," I'd wager, but interesting nonetheless.
I would probably disagree with the statement. I am sure you can find many different takers to voice support of it, but I am not entirely certain that poetry "began" with Whitman and Dickinson. Since the statement does not specify what context of poetry is being discussed, I am even more likely to not support it. If the issue is "poetry" as a genre, there are others who can be considered to be "founders" of it. Even with American Poetic expression, I think that a case could be made that poets like Longfellow or Emerson did more to enhance the American ethic of poetry than Dickinson and Whitman. If one did voice support of the statement, it might be within the idea that both express the notion of the subjective in a unique way to American poetry. Both Dickinson and Whitman speak passionately to the basic idea of what it means to be an individual. For Dickinson, individuality is the ability to examine the world in any way one wishes, while for Whitman, it is to see oneself as a part of a broader fabric where diversity and zeal for American vistas are integral to one's notion of self. It might be here where one could assert the argument. Yet, I think that Dickinson and Whitman did not see themselves as the "founders" of poetry. Dickinson was much more interested in expressing her own thoughts and expanding what she thought to be the fundamental notion of her sense of self. I don't think that she saw this to be something upon which American poetry needed to be founded. While Whitman had little problem expressing his greatness, I think that he would rather see himself as a voice of a new founding of America, and not one of mere poetry. Whitman would see being the founder of the promise and possibility of America as something more lasting and meaningful than poetry, which he would consider part of this vision of America. In this light, I guess I would feel that if they did not see themselves as "founders" of poetry, I would have a hard time doing so.