How do billionaires avoid having to pay taxes? Can "normal" people with average incomes do the same thing?
By putting their finances into a complicated legal structure, moving assets and income through various jurisdictions, and lobbying to make that legal. They also employ highly skilled lawyers who understand the tax code and possible loopholes very well.
I'm pretty sure that a "normal" person with average income could reduce their taxes to close to zero by hiring specialist lawyers, but the cost of those lawyers would exceed the tax savings. For a billionaire, the ratio between legal costs and tax savings is different.