Selling on US Amazon from the UK

Hi,
I have a UK company set up, and it is VAT registered. Currently I am selling on UK Amazon, but I would like to start selling on US Amazon also. How does this work? I have been told that I may need to set up a company in the US. I will be buying products from the US, and shipping them to a tax free state for them to be packaged. To my knowledge, VAT is unclaimable from products bought in the US, the VAT will also not be paid for the sales of these products in the US. So for the VAT side, I am under the understanding that it will basically be like I am not VAT registered for products bought, packaged and sold in the US. As for income tax, this will be paid in the UK. So as a summary, all products in the US will be excluded from VAT, and the other taxes are paid in the UK like normal. Am I correct in saying this? Or am I missing something?