Inflation exist because of fiat, for me they are just one.
You must be ignorant of this economics, inflation exists because of an economy, and whether it's fiat or anything else, the price of commodities may still rise. If you heard stories from the olden days when trade-by-barter happened, inflation also happened and it's simply because someone or sector(s) increases the price/value of their commodities/properties to sell and others follow that trend. It might go on like that until the situation is cautioned.
Not even Bitcoin can stop inflation, it's economic-bound. If the whole world stops fiat and starts spending Bitcoin, do you think there will not be inflation? Then you are a joker.
Inflation is induced by the economy and bad policies, not flat, except that people will know the effect through the country's currency (fiat). You guys are only mistaken this because of the investment opportunity in Bitcoin, but this will change if Bitcoin is being spent in place of other currencies.