Dharma is definitely THE place for dyes!! Love them! I've ordered from them several times and they are awesome!!
As far as dyeing chiffon, there probably is a way to dye it with your procion MX fiber reactive dyes. It sounds like you can't use a soda ash soak for it because its sending the Ph level the wrong direction for it to accept the dye. Try using plain white vinegar instead of the soda ash. (the vinegar is an acid, and will lower the Ph) The rest of the dyeing process would be the same, other than I would rinse it out by hand, not in the washing machine. (especially if it is silk chiffon) It may smell a little like vinegar when you are done. Dharma sells Citric Acid which you can use instead of vinegar if you want, but when I dyed some headbands using a vinegar soak, I simply soaked them in water with a little bit of scented shower gel in it (AFTER the dye was set) and they came out smelling great!
Hope this helps!