It can't. State and local governments can levy their own tax at whatever rate they want and the federal government cannot do anything about it. So the federal sales tax would be on top of all other taxes.
You’re correct. There is no basis to believe that the national sales tax would eliminate state and local sales taxes. However, and this is why all the “it will hurt the poor” arguments begin to crumble, because we are talking percentage here and not hard numbers, those state and local taxes will be reduced as the price of goods and services significantly drops DUE TO THE REDUCTION IN CORPORATE TAXES.