I can think of a couple of solutions that you could try, depending on the effect you want and how much trouble you want to go through.
The simplest would be to wear tan-colored tights, possibly painting a light wood grain on them for effect. This won’t create the flat popsicle stick effect, but it will create a wood effect.
If you want to appear flat, you can make piece like armor pieces that don’t curve around your leg, but are jointed at the knee. These would attach with straps around your legs and be flat on the front side, so you would only be able to pose at specific angles. I would do a flat piece for the thigh, a piece for the knecap, and a piece for the shin, though you may be able to lengthen the thigh piece enough to cover the knee without hindering movement. If you can make these pieces line up in a way that makes them appear flat, such as having them able to interlock, that would be best.
If you wanted them to appear flat from the side but not the front, all you would need is a single joint (think like a brad holding together two pieces of paper) that the pieces can rotate around as you move.
If you don’t mind some degree of encumberment to your movement and want a very flat look, you can create flat pieces that go from your hip to just above your ankle but are only attached to your thigh. When you walk, your calves will be free, though you will have a large, stiff board in front of your leg and will need to still be careful. (I may have just walked around my room a few times with a roll of foam strapped to my thigh to test the feasibility of this – not ideal movement, but not as bad as expected as long as it doesn’t get in the way of your hip joints.)
For materials: cardboard or foamboard or is a good, cheap, lightweight standby. Not the sturdiest, but also won’t hurt if something goes wrong with bending. EVA foam/craft foam would also work, but would need to be prevented from curling or bending. Plastics will be stiffer and more durable, but will also be heavier and might hurt if you walk into something or someone. A thin, lightweight wood (like balsa) would be stiff and have the most realism in texture, but won’t be as sturdy.
I hope that helps! Good luck :]