Down converting 720 24p AIC Footage
 

After I do an FCP edit with 720 24p AIC footage, I bring a 720 24p AIC quicktime it into a DV 720x480 29.97 timeline and export it to this
downconverted format. Only one problem, I get this kind of
mild flickering during playback on an NTSC monitor.

Should I be using Cinematools or Compressor with a proper setting
for a quality downconverted dv/sd video?

Yes. Downconverting that way will introduce artifacts.
Try converting the 24p to 29.97 first using Cinema-tools.
Then downconvert.