Will flat paint work over semigloss paint?

There are flat paints that are made to go over semigloss paint. Many inexpensive flat paints will peel almost immediately when laid over semigloss. The most common solution is to roughen the surface of the semigloss (sandpaper, sandblasting, steel wool, or trisodium phosphate). The actual requirement is to remove alkyds which migrate to the surface of some semigloss and gloss paints. The alkyds make it impossible for latex or acrylic to bond to the surface underneath. You also have to remove buildup of dirt, mildew, etc.

Most primers are suitable for recoating semigloss. Read the label. A layer of primer followed by your flat paint is generally the best solution if the surface is relatively clean. Benjamin Moore Fresh Start interior / exterior acrylic primer is one example of a good primer for this application.