According to one article, there are three sales tax issues to tackle for sellers on Amazon.
Tax nexus - "Ecommerce sellers typically need to consider where they have physical offices and call centers — although many states include other factors, such as affiliates in that state and the location of Fulfillment by Amazon warehouses and whether those warehouses constitute nexus for FBA sellers."
Collecting the tax - "Amazon will charge sellers a fee of approximately 2.9 percent of the collected sales tax. The seller is responsible for getting a sales tax ID number from each state where tax is to be collected. Then the seller has to add the tax ID number(s) into seller support, then the seller either has to click the tax manager page’s use default product tax code box with the correct tax code, or assign each of its listings one at a time with a proper tax code so that the sales of those products are properly taxed."
Paying the tax - Sales and use tax automation: the Vertex Inc. solution keeps track of tax rates and rules "and offer(s) a streamlined process for sellers to make their tax payments quickly, on-time, and in full."
Vertex Inc. is dedicated to small and medium-sized businesses. Vertex Inc. offers a cloud-based sales tax solution that is designed to save time, effort, and risk associated with calculation, return, remittance, and compliance for small to medium-sized businesses.