Building a soft
flat is easy, building a double sided
flat is easy, self standing flats often aren't easy at all... Do the flats need to fit side-by-side seamlessly, or are they independent background items? If they're completely separate and independent from each other, you could attach a plywood triangle about 2' wide (or wider) at the bottom on each side for the
flat to act as a front/back kickstand
base for the
flat. This would be fairly stable and look the same from both sides, but will be visible to the audience at all times (might get by with a slightly wider triangle on one side only).
Another option would be booking two flats together with double-swing hinges. This would let you fold the flats together to turn them, then
swing the two apart like opening a
book. Leaving them at a 90-ish degree angle to each other (like a half-open
book) allows them to stabilize each other. The double
swing hinges (think wild west saloon doors) would let you
book them in either direction.
Another thought, if you have room onstage and in the budget for a little more carpentry, is making three flats into a triangle shape (known as a '
periaktoi'). No hinges to flip, no kickstands sticking out, you can
butt them up against each other fairly tightly, you can mount them on wheels to spin them, or use handles or straps to lift them and turn them manually.
If the flats stay
in one location and just have to spin, sometimes it works to mount a vertical pipe to the floor and slide the
flat down onto the pipe via holes drilled through the center of the
flat frame. However, getting a sufficiently rigid connection to the floor can be a challenge (ceilings usually aren't low enough to help for bracing), and this construction in general is a
bit more advanced.
10 year olds for crew? I see your interest in light weight construction. There should be plenty of articles here about soft
flat construction, and you might think about corrugated cardboard as well, if it's a short run, low budget show. Refrigerator boxes are one option, plus if there's a packaging company near you they might have large sheets of unfolded cardboard (I've been able to get a large quantities of misprinted boxes for free from such places) Foamcore would be another option, but pricey for large sheets.