Answer:
US standard quarts
If you are asking about US quarts, they have 32 ounces and each ounce equals 28.35 milliliters, so one US quart must be 32 x 28.35 = 907.2 milliliters.
So 1 milliliter must be equal to 1/907.2 = 0.0011022 US quarts.
UK standard quarts
If you are asking about UK quarts, they have 40 ounces and each ounce equals 28.35 milliliters, so one UK quart must be 40 x 28.35 = 1134 milliliters.
So 1 milliliter must be equal to 1/1134 = 0.0008818 UK quarts.