I did once try to cut a “living hinge” on a piece of MDF that had a veneer of quilted maple glued to the top. I was trying to make something like this, but without paying the price of a 1/8 thick piece of solid wood:
Unfortunately, it did not work very well. The cuts in the living hinge were too close together and the glue holding the veneer on those parts did not hold well. So lots of small veneer pieces flaked off in the hinge part. I would not recommend doing living hinges with a veneered piece of wood.
If you want to make living hinges I suggest solid pieces of wood.