If you want it done right spend the money on a real matte from HOK. The issue with most flat colors is they are porous meaning they absorb water which isnt good for the paint or the metal.
From my limited knowledge I dont know of a way to protect the paint other than putting a clear coat on it but that means your flat look is gone.
BASF makes a line of paint that has flat base with a matte finish…basically a satin finish…flat color with a protective layer (matte clear). Basically what you wanted