Semi gloss and flat paints can be mixed together and the result will be an eggshell or satin finish, depending on how much of each you mix. While many different paints can be mixed together, there are some instances where it won't work at all.
Generally, it's fine to mix paints together as long as they are both the same base. You can mix water-based paints together and oil-based paints together but mixing oil- and water-based paints works about as well as mixing regular oil and water. Similarly, it is possible to mix exterior and interior paints together but rarely advisable, unless painting the interior of a shed or some other space where functionality is not important. Never use exterior paint inside, or interior paint outside, no matter what the gloss is. Neither will hold up well. It is fine to mix different brands of paint together, as long as they have a compatible base.
Mixing flat and semi gloss (or semi gloss and satin, or flat and eggshell, or any mix of glosses) works best if you are very thorough in mixing the two. Pour both paints into a completely separate clean container and mix with a stir stick or mixer attached to a drill. Failing to mix it completely may result in different sheens apparent between the brushing and the rolling. Make sure you have enough paint mixed for your project because a paint store will be unable to match it for you and it will probably be impossible for you to match the sheen perfectly yourself in a later batch.
While mixing semi gloss and flat paints together may give you a more washable surface than just flat alone, don't assume this will be the case. All paints are carefully formulated to perform when applied as directed, and mixing two types together won't necessarily give you a more washable finish merely be increasing the sheen. Much depends on the quality of each paint.
Using interior paint on outdoor surfaces, even when mixed with exterior paint of any gloss, guarantees you a paint job that won't last long. Exterior paint does not work as well on interior surfaces because it is not designed to be cleaned and because it is higher in volatile organic compounds, meaning it will give off potentially harmful fumes for weeks as it cures. Each type of paint was developed with a function in mind, from flat ceiling paint to high gloss trim paint. Mixing the two will negate the function of each and while it may look fine, don't expect the finished product to perform as well as intended.
There is no science in mixing flat and semi gloss paints together. It is more of an art and much depends on the individual paint type and quality. Mixing one gallon of cheap flat ceiling paint with one gallon of semi gloss trim paint will very likely get you a different sheen than mixing a gallon of high quality flat wall paint with the same gallon of semi gloss trim paint. Much depends on the binders used, the amount of titanium oxide in each paint formulation and any additives used for leveling and mildew resistance.