I've got one of those part polyester part cotton hakamas (30%/70% I think). I stuck it in the machine and washed it alone. Then gave it a spin at reduced number of rpm's.
Finally I took it out folded the pleats, secured them in the botton with clothes-pegs, attached the top to a coat hanger and hang the whole thin up to dry in my shower booth. It seemed to work allright.
If your hakama is pure polyester, I think you could just wash it in the machine.