You have three ridiculous-sounding options. Option one: Let the water sit in a pitcher in the fridge overnight. The minerals will sink, and you can pour off the top like a fancy water sommelier.
Option two: Boil the water and let it cool. This forces the calcium to come out of solution, forming a white crust on the pot. You’re basically mining your own limestone quarry. Scrape it out and pretend you’re a medieval peasant.
Option three: Buy a water filter. A simple Brita pitcher or a faucet filter will catch the flakes and give you water that looks like a wealthy person’s tears.