You really have 3 areas that are eliminated.
1) Personal withholding (matched by employer)
2) Corporate compliance cost
3) Corporate income tax
By eliminating the withholding, your take home pay increases. By eliminating employer matching either your pay increases or the employer's cost decreases. By eliminating compliance costs, the cost decreases. By eliminating corporate income tax, cost decreases.
I suspect you might have forgotten the 3rd element. Either way, the decrease in cost can either be used to increase profits or to decrease price. Given a free, competitive market, the price will fall.
The actual percentage of cost reduction can be debated and has been debated. However, it is clear that a cost reduction will occur.
I don't disagree that some price reduction will occur. I just don't see any beyond a portion of corporate income taxes (not all of them) the employer's share of FICA and the elimination of compliance costs. The latter two don't represent but a tiny part of the final product's price. The former comprises the larger part. IMO, any significant decrease in prices can only come from lowered wages and that can't jhappen in some cases (union shops).
Now OHelix gave an example earlier which included the cascade effect. Let me put my spin on it: Bike Company buys it pedals from company A, it's tires from company B, its frames from company C and its seats from company D and all have been profitable companies in the past and are paying a 35% corp tax rate. With the flat tax they each retain an extra 10% of their profit now. They choose to lower their prices each by 10%. Now we have Bike Company's cost of goods, which represents 50% of its production cost, lower by 10%. Also: Bike Company now pays no income taxes, thereby saving itself another 10% a year. Am I missing something or did Bike Company just come up with a way to lower its prices by 15%. Am I on the right page OH?