If the distribution is in another state, Amazon will not charge sales tax.
The way it works, if Amazon, or anyone for that matter, has a shipping facility in your state, you have to pay state tax, and that will be done via the merchant. So, when that distribution center goes live, Amazon will have to do some pretty good pricing because they will have to charge shipping AND sales tax. Unless Amazon, with shipping and tax, can come in lower than the local B&M, it may work to their benefit.
They are talking about setting up a shipping center here in Jersey and, when it goes on line, we'll have to pay sales tax and shipping* as well. As for reporting out of state purchases, when they find some way to require vendors to report their sales to every customer in every state to the state, then it'll happen. Right now, that's not a requirement. There is no means of tracking it. Tax preparers can ask, but if they don't say, there's no way for the state to know.
*Amazon Prime members can get free shipping from some merchants.