How much of the higher price of gasoline is the Fed's fault?

To a first approximation, zero. Oil is priced in dollars in the international market. The falling dollar has no effect on the price of oil. And inflation is a tiny contributor to the huge increase in gasoline prices. The huge increase is due to the fact that a lot of people want to consume oil, but producers have been slow to supply additional quantities. When demand goes up and supply doesn't, prices rise.