There is a link between higher gold prices and inflation, but they are not directly related. Confusion arises from misunderstanding inflation and its consequences.
Inflation is the deliberate devaluation of money by the government and central banks. Inflation is achieved by increasing the money supply and credit. All governments inflate and destroy their own currencies. Devaluation of money, that is, inflation, leads to a decrease in the value of money in circulation. This leads to a loss of purchasing power, which over time is reflected in higher prices for most goods and services. Higher prices are a consequence of inflation. These effects are volatile and unpredictable.
This makes it difficult to use simple financial and economic statistics, makes it difficult to make routine business decisions, distorts financial planning forecasts, and distorts the business cycle. The shift in the business cycle is a result of the Fed's efforts to manage the phases of the business cycle to avoid recessions and depression, but it does its job poorly. Indeed, the Fed tends to create the very recessions and depressions that it is allegedly trying to avoid.