This is not what inflation is. Inflation is bad for rich people because the value of their wealth hoards decreases, but what this actually is (wildly increasing rent and prices of groceries) is just (legal) profiteering if anything.
Edit: it appears I was mistaken. Please disregard this post.
Rich people aren’t just hoarding money in a bank like Scruge Mcduck, unless they’re not very smart. If most of their money was tied into bank bonds that didn’t out perform inflation, then it’s bad for them. But if it’s tied to business stock or ownership, then those stocks are now worth more money for one to be willing to give up that stock. Inflation benefits some types and hurts others.
Rich people do not hoard cash. Their assets appreciate as more profit is realized from the inflation (which is always accompanied by, and often caused by, price gouging). Line go up. They win every time.