Attend to the marker stain as soon as you see it. You have a better chance of getting the marker stain off flat paint if you clean it before it dries and settles.
Mix baking soda and white toothpaste in a bowl. Mix enough to cover the marker stain.
Use paper towels to apply the baking soda and white toothpaste mixture on the marker stain. You must be meticulous and only apply this mixture to the area that has the marker stain. Leave the mixture on the marker stain for 10 minutes so that ink from the marker loosens.
Apply water to a clean white cloth and squeeze the excess liquid from it. Gently remove the mixture you applied on the marker stain by scrubbing it off. Switch to a clean part of the cloth when the part you are using to scrub becomes dirty. Make sure to only scrub the affected area. Repeat as necessary.
Clean the marker stain area with another damp cloth to clean any residue. Dry the area by blotting with a towel. Be advised that depending on the quality of your flat paint, you may see paint discoloration or dullness in the affected area. This will be better than a marker stain, however.