Unfortunately, I'm a bit pressed for time at the moment to give you a fresh and detailed answer, but a couple of months ago someone asked a very similar question to this, which I answered here (I've also written a refutation of a very popular book by Edward Baptist that makes the counter-claim here, with supporting references to other critiques). The short answer is that slavery is certainly significant, it is not at all definitive; that is to say, you cannot (in my view) pick slavery out from the historical record and say "this is essential for the United States becoming a thriving capitalist economy and without it, the United States would not be nearly as economically successful today". The evidene just doesn't suggest that. It has a role to play, yes, but the evidence that slavery was intrinsic to industrialisation - that it would have somehow been implausible without slave profits - of the northern United States is mixed and weak. In the case of the Southern US, the long-term legacy of slavery is one of economic stagnation and disadvantage rather than prosperity.

In essence: slavery creates vast quantities of wealth, but that does not translate into significant economic prosperity. Most of the money slavery created remained trapped within the slave system and disappeared with the forced abolition of slavery during and after the Civil War. In the modern world it actually does the opposite: extreme forms of unfree labour have been shown to depress both local and national economies rather than stimulate them. Whilst abolition does seem to have an impact on the immediate economic health of the United States, there is no evidence of a significant economic collapse post-1865; the US economy recovers very quickly from both slavery's abolition and the end of the Civil War.

What the experience of slavery does explain much better is the structure of the US economy and the distribution of wealth within it; that is to say, it doesn't account itself for how prosperous the United States is in 2016, but it does help to explain who benefits from that prosperity. The disproportionately high poverty rate among African Americans can largely be explained by looking at the legacy of slavery and the failures of the way in which emancipation was carried out; racial prejudice itself is a legacy of slavery, and many racial stereotypes concerning African Americans can be traced back to justifications and rationalisations for holding black people as slaves. Slavery's economic and social legacy is very real and alive today, just not in the sense that the United States unequivocally owes its 20th and 21st Century prosperity to the institution of slavery.