Flat is not a color. It refers to gloss or sheen, or more specifically a lack there of. Flat paint is the least durable. That’s why it is only used on ceilings. You should at least use a satin.
If you don’t really care what color white it is ask for the untinted paint base. The color of the untinted paint base will vary from manufacturer to manufacturer and also over time as they are using the cheapest crap they can for the base. Tthe untainted base may be cheaper as it is the pigments that are the most expensive component of the paint. All of the paint manufacturers colors that you see on their website are purposely designed to be mixed with affordable pigments. Getting a custom color match can double the price of a gallon of paint sometimes
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