Because his income is almost nonexistent. He is worth, what, $100b? He doesn't MAKE $100b.
Almost all of his assets are tied to the valuation of stocks/companies. If he sells his Berkshire A stock, now almost $500k per share, he would pay taxes on whatever gains he incurred.
For example, you buy $1000 of Amazon stock at their IPO date back in 1997. Today that same stock you bought for $1000 is now worth about $1.1m. You don't pay taxes on the million dollar gains until you sell the stock. And the long term capital gains tax rate, any investment held for 366+ days, is maxed at 20% (for high income earners which WB is purposely not one). The highest income tax marginal rate is 37% or so.
He has structured his income to come from assets like municipal bonds (tax-exempt interest and available to anyone).
Sure he has people working for him to figure this out that normal people like us can't afford to pay, but what he is doing isn't anything we couldn't.