Best way to measure inflation in real time?
The highest frequency real time data that I am aware of the Billion Prices Project, which is daily. Link to website. These are prices on the internet, which can be mapped to the US CPI relatively well.

Otherwise, consumer prices in bricks and mortar stores are Generally not set “minute by minute,” nor is there a way to sample them at that frequency. 

The closest you can get is countries in hyperinflation, where prices end up being indexed to a foreign currency. That is, the price paid is a fixed price in a foreign currency, multiplied by the exchange rate. This mechanism results in rapid changes, even during the time to drink a coffee (anecdote from the Weimar hyperinflation). Foreign exchange rates are the usual way of estimating a hyperinflation, since there is no good way to survey prices.