No, it's actually not.
Imagine you earn $30,000 a month compared to someone who earns $200,000 a month.
If I put an income tax of 20% on both of these, then the $30,000 will pay $6,000 in tax and the $200,000 will pay $40,0000 in tax
If I put a sales tax of 20% on items instead, the $30,000 will end up paying $6,000 in tax because they're going to spend all their money. The $200,000 might only spend $50,000, and therefore they're going to be paying $10,000 in tax.
In reality if you just had sales tax, it would need to be HIGHER than if you just had income tax, because you make more money from income tax than sales tax. So, a poor person who spends all their money will pay more.
Your argument is a wrong one. You're trying to say that the rich pay so much in income tax, they do, because they earn most of the money. However as a percentage of money that someone has, the rich are paying far, far less.
Also, the more money poor people have, the more they will buy (up to a certain amount), therefore more things will be bought, more things will be bought, meaning money is flowing more.