Whenever the flat tax is mentioned the employer/business tax is NOT mentioned, even though it will probably increase the cost of goods.
That would be 24% lower than the current corporate income tax, so it's very hard to see how prices would increase. It's also very hard to cheat that kind of a tax by offshoring. You have to pay it where the sale occurs, not where you park a headquarters building.
It will increase the cost of goods in some circumstances, but more importantly it will burden small business start ups and individual entrepreneurs. Imagine starting a small business - you'll have to pay the 16% tax on gross sales even if your business is losing money. For self employed individuals the tax rate is 26% not 10%. And in order to collect that tax the government will have to establish an extensive and intrusive tax collection process that tracks sales and gross receipts for every transaction.
Sen. Cruz may shut down the IRS but he'll have to replace it with an even more intrusive organization. Maybe he can call it the SS, or the KGB, or STASI.