While you may indeed THINK that (and while some -- like FairTax shills -- want you to believe that) it simply is not the case. ALL Federal taxes, embedded or not, wind up as Federal Tax Revenue. That number is easy to find; any report on the Federal Budget will provide the data for any year you choose.
As shown in Post #23 the combination of Personal Income Tax and FICA taxes represents about 80% of all Federal Tax Revenue ... and is growing as a consequence of the rise in Social Security funding/spending.
It is near impossible to know just how much of the cost of a good is inflated ...
Actually, it's not all that hard to figure it out. Data is available to anyone who wants to look that lays out what the components of the aggregate price level are ... taxes, labor, capital, profits, interest, etc. To summarize such analysys, which has been repeated countless times on these threads, Corporate Taxes represent less than 2% of the price of goods. The Employer part of FICA tax represents about 4% of the price of goods. Costs of compliance with the Tax Code represent about 1% to 2% of the costs of goods. In total, if ALL Corporate taxes, ALL Employer paid FICA taxes, and ALL compliance cost savings are returned to the Consumer through price reductions, price can only adjust, AT MOST, about 7.5% (before the addition of the 30% FairTax.) In reality, some portion of these sums will likely remain in price to be put to other business uses.
...due to the need to make a profit by each contributor to the production of a product, which is affected by taxation at each stage.
Actually you have the cause and effect backwards. The "need to make a profit" is not affected by taxation. Taxes are affected by profit: small profit, small tax. Large profit, large tax. The need to make a profit is what drives businesses to lower costs. The market drives prices. What's left over from the two is profit ... and a portion of profit is peeled off as tax ... just like your wages. Your wages are not "inflated" due to your need to have income; taxes affect the cost of labor in the same way they affect the cost of goods.
If you want to lower your tax burden (hidden or otherwise) you first need to lower government spending. The method of collection is secondary.
Have you checked your phone or cable tv bill lately?