I use iDye Poly to dye chiffon flowers & trim - its specifically made for polyester and nylon and the results are vibrant. It's a super easy process (everything's in the packet!) and the colors come out nice and rich. The only drawback is it's only available in 8 colors
Acid dyes didn't work well for me - I got very pastel results even after dying the chiffon multiple times.
Here's some flowers I dyed with iDye Poly