However, it kind of sounds like you're talking about a stitch done with a double needle; on the top, you would see two straight lines of stitching, on the bottom, the bobbin thread zig zags from one to the other.
It's the framework that's going to be a challenge. I would try to find the heaviest, stiffest wire I could bend--maybe even double or triple strands. To get the nice round edges, check hardware store for pipe insulation; it is usually slit all along its length. put the wire in, seal it up with the sticky stuff, then make a leaf shape. See the cross-bracing on each leaf? It could be something rigid, like a dowel or PVC pipe. Put it at the widest part of each leaf, plus anywhere else that seems to need it. Cover with fabric; easiest would probably be cover only the lower side, bring the fabric snugly around the frame, and stitch in place. Glue will likely bleed through and look ugly, but you could test it out on scrap. Trim off any excess fabric as you go. Figure how to stabilize the floor end; maybe a heavy cardboard tube, or a tall wastebasket. I'll call this "the can" Fasten it to the floor, or at least to a heavy chunk of plywood. Shape the centermost leaf approximately how you want it.
GET AT LEAST ONE OR TWO PEOPLE TO HELP YOU FROM HERE ON OUT
Put the leaf end into the can. Have one or two people hold the leaf up how you want it to be, and another person uses a ladder to suspend the leaf from the ceiling with fishing line in several places.
Repeat for each leaf, then attach the surrounding pieces (they look like sepals to me, but I think that's what you called the trunk). They look like they're built pretty much like the leaves, but with a center rib to give them dimension.
Disclaimer: I've never done anything like this, I'm just trying to figure out what I'd try first. I would buy enough materials to make one leaf and see how it worked out before investing in the rest.
Incidentally, you might want to check with the fire department; we got in trouble one time for having banners hanging below the sprinklers, so there may be some law or regulation in your area. Take a picture with you, that should entertain them!
I'm thinking decals. You can buy decal paper, print from your computer, then water-transfer the image; the gold (or whatever) color of the locket would show through. You'd probably need to put a tough finish on the top so they don't get scratched.