From my theater days, we built flats by making a 4' x 8' frame out of 1"x3" wood, then took some 1/4" plywood and cut 6" triangles which we naild to the corners to keep everything square. The canvas or muslin was wrapped around the flat and nailed on the back side.
When I ran a video production studio, we made more elaborate "flats" which we used to create the walls of a kitchen, livingroom, etc. For that we nailed drywall (sheetrock or paneling) to a 2x4 frame, then braced the back with "two wings" made of of 2x4. We made some as walls, some with windows, etc. We would bolt these flats together, paint them, shoot our videos, then pull them apart, and re-assemble them as necessary. Some even were built on casters so they could roll into the studio. I'm sure there are books or websites with plans for all types of flats. If not, contact me and I'll send you a diagram.
Marty
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