In a sense, inflation does not follow the law of one price. That is, there is nothing that says that countries will come to have similar inflation rates due to the law of one price. However, there is a connection between the law of one price and inflation.
The connection comes through exchange rates. The law of one price implies that relative levels of inflation in two countries will be reflected in their exchange rates. The law of one price is extended by the idea of purchasing power parity. Purchasing power parity, in turn, implies that exchange rates and interest rates will be connected. If Country A's inflation rate is (for example) 2 percentage points above that of Country B, country A's currency should depreciate by 2 percentage points per year relative to Country B's.
In this way, the law of one price does have implications for inflation.